Sequence Guess

Guess the sequence. The solutions is near.

Sequence: 1 1 2 300 49500 458865000 102230762782500000 34830764014069530200306250000000 24508729252705420391522596737223740542435574843750000000000 1309051266892045245099291618442119121030355180569577769830415276675027646361844993307869140625000000000000000 16762226679237960636007550244784386640519707585527065881996179947890157239530242446388633763274371100329528601245504122822223309483127880934989561689505573827946824167907714843750000000000000000000000 8066783810216193100063883436181463933530529496778882468203848624838224689869650437854990633028185201091980847193038933668519423460468940644633768037921728237627151565987127625683052816238973207773865067695353412425074981848519676055484029638669276041353808287964060850995131789679729748306434520820492384846323693907528448104858398437500000000000000000000000000000000 2655094859052430648798226389816372320723928936126657357956521171735778310999056058985380254642423664998782587901975989679503069095667350466650104725161906131456377030815382143025492234931994143197165374550689610956958865514970425788182461846828245984031993894651255997428222568717129989661811304565241039941216943160764325439877497507161057701643202479907819367603899212650144897098330880263743104022189166163466026433375647048630420487938820742798241223507768922306288586111452715953505286349695459350970691030483810273905770285203654154297108493466396580890455856185998315534527622703811713812584220349142793565988540649414062500000000000000000000000000000000000000000000000

Solution

The solution is:

2655094859052430648798226389816372320723928936126657357956521171735778310999056058985380254642423664998782587901975989679503069095667350466650104725161906131456377030815382143025492234931994143197165374550689610956958865514970425788182461846828245984031993894651255997428222568717129989661811304565241039941216943160764325439877497507161057701643202479907819367603899212650144897098330880263743104022189166163466026433375647048630420487938820742798241223507768922306288586111452715953505286349695459350970691030483810273905770285203654154297108493466396580890455856185998315534527622703811713812584220349142793565988540649414062500000000000000000000000000000000000000000000000 5385219730395789494499985942861818154333286511291833239602616210773952968875555129629657469970040632379233601869676910707014014116097576602424864756942670183028456858896531311872461551450264902306309872773638793850864681357731956355170715971117124718720763115404081428832792230388203661463565286752137736615772220345106110925915705862299577034130628456470376318865621069699333028091314055557630066741968106928170877356046283552373813139138235445717271446392372299518558433315963931561741317051246506696882592192989148253270153774324645870552087669975134412857610549192015537178129611247288086321812013610933662590406479820881241596711320388003841213777614116882670095195549089942902352602696351565672654763659234382443727062550965290763957017652887860510623850741986677127334349599636118670083940774566574364343477553710034213409116670008490872836458428734370240187529220613278643771493654087607471557932355200477896383781003699727299796368512593022079556625415725190202646268766302470110865540211231780492953753047159158036242592666296341336920319984120753676477260324775416560411578809729670964555582237766647239084486355589151182943336808790490977116860449314117431640625000000000000000000000000000000000000000000000000000000000000000000000

And the recurrence formula is

 (seq[-1] * 5) * (seq[-2] + 9) * (seq[-3] * 3)

This fine program was brought to you by hakank@bonetmail.com
My other useless programs.