A137219 a(n) = (A126086(n) - 3*A001850(n) + 2)/6.

1, 62, 2649, 116360, 5364701, 256452714, 12582472897, 629389744448, 31955247002601, 1641724953315062, 85159811841234857, 4452782349569991736, 234393562418967430389, 12409423916979629786322, 660253088667210584565249

Offset: 1

Author

Vladeta Jovovic, Mar 06 2008, Mar 16 2008

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A001850, A047665, A126086, A137220.

Programs

Maple

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

Mathematica

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];
A137219[n_]:= (A126086[n] - 3*A001850[n] + 2)/6;
Table[A137219[n], {n, 30}] (* G. C. Greubel, Jan 05 2022 *)

Sage

def A137219(n): return round( sum( binomial(binomial(j, n), 3)/2^(j+1) for j in (0..1000) ) )
[A137219(n) for n in (1..30)] # G. C. Greubel, Jan 05 2022

Formula

a(n) = Sum_{m >= 0} binomial(binomial(m, n), 3)/2^(m+1).

Extensions

More terms from R. J. Mathar, Apr 01 2008