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1, 62, 2649, 116360, 5364701, 256452714, 12582472897, 629389744448, 31955247002601, 1641724953315062, 85159811841234857, 4452782349569991736, 234393562418967430389, 12409423916979629786322, 660253088667210584565249
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{m >= 0} binomial(binomial(m, n), 3)/2^(m+1).
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MAPLE
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A126086 := proc(n) local x, y, z ; coeftayl(coeftayl(coeftayl(1/(1-x-y-z-x*y-x*z-y*z-x*y*z), z=0, n), y=0, n), x=0, n) ; end: A001850 := proc(n) local k ; add(binomial(n, k)*binomial(n+k, k), k=0..n) ; end: A137219 := proc(n) (A126086(n)-3*A001850(n)+2)/6 ; end: seq(A137219(n), n=1..30) ; # R. J. Mathar, Apr 01 2008
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MATHEMATICA
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A126086[n_]:= A126086[n]= Sum[(-1)^k*Binomial[n+k, n]*HypergeometricPFQ[{-k, n+1, n+1}, {1, 1}, 1], {k, 0, 2*n}];
A001850[n_]:= Hypergeometric2F1[-n, n+1, 1, -1];
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PROG
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(Sage)
def A137219(n): return round( sum( binomial(binomial(j, n), 3)/2^(j+1) for j in (0..1000) ) )
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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