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
KEYWORD
nonn
AUTHOR
Michael Somos, Mar 12 2014
STATUS
approved