A239226 a(n) = A000984(n) * A081085(n).

1, 8, 120, 2240, 47320, 1084608, 26330304, 666631680, 17419647960, 466416716480, 12730856057920, 352914423912960, 9908504597118400, 281166914888384000, 8050729214434752000, 232310201739468042240, 6748710905805484610520, 197211871554285957969600

Offset

0,2

Comments

Denoted s_4B by Piezas.

Links

G. C. Greubel, Table of n, a(n) for n = 0..665

Wikipedia, Ramanujan-Sato series.

Formula

D-finite with recurrence 0 = a(n) * n^3 - a(n-1) * 8 * (2*n - 1) * (3*n^2 - 3*n + 1) + a(n-2) * 128 * (n-1) * (2*n - 1) * (2*n - 3) for all n in Z.

Example

G.f. = 1 + 8*x + 120*x^2 + 2240*x^3 + 47320*x^4 + 1084608*x^5 + 26330304*x^6 + ...

Mathematica

Table[Binomial[2*n, n]*Sum[Binomial[n, k]*Binomial[2*k, k]*Binomial[2*n - 2*k, n - k], {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Aug 07 2018 *)

Prog

(PARI) {a(n) = binomial(2*n, n) * sum(k=0, n, binomial(n, k) * binomial(2*k, k) * binomial(2*n - 2*k, n-k))};
(Magma) [Binomial(2*n, n)*(&+[Binomial(n, k)*Binomial(2*k, k)*Binomial(2*n - 2*k, n - k): k in [0..n]]): n in [0..50]]; // G. C. Greubel, Aug 07 2018

Crossrefs

Cf. A000984, A081085.

Sequence in context: A004381 A166179 A130979 * A133308 A191098 A151834

Adjacent sequences: A239223 A239224 A239225 * A239227 A239228 A239229

Keyword

nonn

Author

Michael Somos, Mar 12 2014

Status

approved