A300116 a(n) = Sum_{k=0..n} binomial(2k,k)^3 * binomial(2n-2k,n-k) * 2^(4*(n-k)).

1, 40, 2008, 109120, 6173656, 357903040, 21090174400, 1257411781120, 75630327895000, 4580277582101440, 278915640538355008, 17061127317021130240, 1047543937631077672384, 64523332938885758410240, 3985152917145136901283328, 246717298245058901071237120

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..554

Wadim Zudilin, Ramanujan-type formulae for 1/π: A second wind?, arXiv:0712.1332v2 [math.NT], 2008.

Formula

n^3 * a(n) = 8 * (2*n-1) * (8*n^2-8*n+5) * a(n-1) - 4096 * (n-1)^3 * a(n-2) for n > 1.

a(n) ~ Gamma(1/4)^4 * 2^(6*n - 2) / (Pi^(7/2) * sqrt(n)). - Vaclav Kotesovec, Jul 10 2021

Prog

(PARI) {a(n) = sum(k=0, n, binomial(2*k, k)^3*binomial(2*n-2*k, n-k)*2^(4*(n-k)))}

Crossrefs

Cf. A036917.

Sequence in context: A190076 A278729 A189550 * A060056 A223177 A140729

Adjacent sequences: A300113 A300114 A300115 * A300117 A300118 A300119

Keyword

nonn

Author

Seiichi Manyama, Feb 25 2018

Status

approved