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%I #14 Mar 17 2020 12:09:27
%S 20,8464,4050864,2116980800,1173644492800,678353946298560,
%T 404352269157205152,246796318508780847360,153477802845690943118400,
%U 96903346351876187722368000,61954834924471706682462940800,40029904663914104968204952365824,26096917229103772343967114415006304
%N a(n) = A181544(2n, 2n-1).
%H David J. Gross and Vladimir Rosenhaus, <a href="https://arxiv.org/abs/1702.08016">The Bulk Dual of SYK: Cubic Couplings</a>, arXiv:1702.08016 [hep-th], 2017, p. 33.
%t t[n_, k_] := SeriesCoefficient[Sum[Binomial[n + j, j]^3 x^j, {j, 0, n + k}] (1 - x)^(3n + 1), {x, 0, k}];
%t a[n_] := t[2n, 2n - 1];
%t Array[a, 13] (* _Jean-François Alcover_, Feb 14 2019 *)
%o (Sage)
%o def a(n) :
%o R.<x> = QQ[]; p = 2*n; q = 2*n-1
%o return ((1-x)^(3*p+1) * sum(binomial(p+r,r)^3 * x^r for r in [0..p+q]))[q]
%K nonn
%O 1,1
%A _Eric M. Schmidt_, Oct 04 2017
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