cp's OEIS Frontend

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

%I A239226 #11 Sep 08 2022 08:46:07
%S A239226 1,8,120,2240,47320,1084608,26330304,666631680,17419647960,
%T A239226 466416716480,12730856057920,352914423912960,9908504597118400,
%U A239226 281166914888384000,8050729214434752000,232310201739468042240,6748710905805484610520,197211871554285957969600
%N A239226 a(n) = A000984(n) * A081085(n).
%C A239226 Denoted s_4B by Piezas.
%H A239226 G. C. Greubel, <a href="/A239226/b239226.txt">Table of n, a(n) for n = 0..665</a>
%H A239226 Wikipedia, <a href="https://en.wikipedia.org/wiki/Ramanujan-Sato_series">Ramanujan-Sato series</a>.
%F A239226 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.
%e A239226 G.f. = 1 + 8*x + 120*x^2 + 2240*x^3 + 47320*x^4 + 1084608*x^5 + 26330304*x^6 + ...
%t A239226 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 *)
%o A239226 (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))};
%o A239226 (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
%Y A239226 Cf. A000984, A081085.
%K A239226 nonn
%O A239226 0,2
%A A239226 _Michael Somos_, Mar 12 2014