A074649 a(0) = 1; for n >= 1, a(n) = sum(binomial(n,k)^3*binomial(n+k,k+1)^2,k = 0..n)/n^2.

1, 2, 23, 434, 10897, 327270, 11076235, 408850370, 16119036965, 669177449258, 28960814900899, 1297024187184478, 59777126587203937, 2822927389747980806, 136132927766691327651, 6685542830954666301218, 333618582889745741654221

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Vaclav Kotesovec, Recurrence (of order 5)

Formula

Special values of the hypergeometric function 5F4, in Maple notation : a(n)= hypergeom([n+1, n+1, -n, -n, -n], [1, 1, 2, 2], -1), n=0, 1...

a(n) ~ c * d^n / n^4, where d = 63.74669588201779948... is the root of the equation -2 - 247*d - 11666*d^2 - 502*d^3 - 53*d^4 + d^5 = 0 and c = 0.3611541... - Vaclav Kotesovec, Mar 02 2014

Mathematica

a[0] = 1; a[n_] := Sum[Binomial[n, k]^3*Binomial[n + k, k + 1]^2, {k, 0, n}]/n^2; Table[a[n], {n, 0, 16}]

Crossrefs

Cf. A074635.

Sequence in context: A338178 A219890 A119774 * A233211 A134355 A187656

Adjacent sequences: A074646 A074647 A074648 * A074650 A074651 A074652

Keyword

nonn

Author

Karol A. Penson, Aug 28 2002

Extensions

Edited by Robert G. Wilson v, Aug 29 2002

Status

approved