A371739 a(n) = Sum_{k=0..n} binomial(5*n,k).

1, 6, 56, 576, 6196, 68406, 768212, 8731848, 100146724, 1156626990, 13432735556, 156713948672, 1835237017324, 21560768699762, 253994850228896, 2999267652451776, 35490014668470052, 420718526924212654, 4995548847105422048, 59402743684137281920

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = [x^n] 1/((1-2*x) * (1-x)^(4*n)).

a(n) ~ 5^(5*n + 1/2) / (3*sqrt(Pi*n) * 2^(8*n - 1/2)). - Vaclav Kotesovec, Apr 05 2024

a(n) = Sum_{k=0..floor(n/2)} binomial(5*n+1,n-2*k). - Seiichi Manyama, Apr 09 2024

a(n) = binomial(1+5*n, n)*hypergeom([1, (1-n)/2, -n/2], [1+2*n, 3/2+2*n], 1). - Stefano Spezia, Apr 09 2024

Mathematica

Table[32^n - Binomial[5*n, 1+n] * Hypergeometric2F1[1, 1 - 4*n, 2+n, -1], {n, 0, 20}] (* Vaclav Kotesovec, Apr 05 2024 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(5*n, k));

Crossrefs

Cf. A032443, A066380, A066381.

Sequence in context: A093142 A092655 A099140 * A048348 A227384 A199755

Adjacent sequences: A371736 A371737 A371738 * A371740 A371741 A371742

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 05 2024

Status

approved