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A137219
a(n) = (A126086(n) - 3*A001850(n) + 2)/6.
3
1, 62, 2649, 116360, 5364701, 256452714, 12582472897, 629389744448, 31955247002601, 1641724953315062, 85159811841234857, 4452782349569991736, 234393562418967430389, 12409423916979629786322, 660253088667210584565249
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{m >= 0} binomial(binomial(m, n), 3)/2^(m+1).
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 *)
PROG
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Mar 06 2008, Mar 16 2008
EXTENSIONS
More terms from R. J. Mathar, Apr 01 2008
STATUS
approved