A218690 Sum_{k=0..n} C(n,k)^4*C(n+k,k)^2.

1, 5, 181, 9797, 616501, 45778505, 3678753205, 314352091205, 28154344881205, 2612340741982505, 249415797821914681, 24374175871569953225, 2428502737999745059381, 245952659136011117909897, 25260608441078125508484181, 2626023605592369669830217797

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

V. Kotesovec, Asymptotic of generalized Apery sequences with powers of binomial coefficients, Nov 04 2012

Formula

a(n) ~ ((1+sqrt(5))/2)^(2*(5*n+4)-3/2)/(5^(1/4)*(2*Pi*n)^(5/2)*sqrt(2)).

Mathematica

Table[Sum[Binomial[n, k]^4*Binomial[n+k, k]^2, {k, 0, n}], {n, 0, 20}]

Crossrefs

Cf. A005258, A218692.

Sequence in context: A053363 A027572 A050239 * A345338 A256286 A304277

Adjacent sequences: A218687 A218688 A218689 * A218691 A218692 A218693

Keyword

nonn

Author

Vaclav Kotesovec, Nov 04 2012

Status

approved