A293286 a(n) = A181544(2n, 2n-1).

20, 8464, 4050864, 2116980800, 1173644492800, 678353946298560, 404352269157205152, 246796318508780847360, 153477802845690943118400, 96903346351876187722368000, 61954834924471706682462940800, 40029904663914104968204952365824, 26096917229103772343967114415006304

Offset: 1

Author

Eric M. Schmidt, Oct 04 2017

Keywords

• nonn

Links

• David J. Gross and Vladimir Rosenhaus, The Bulk Dual of SYK: Cubic Couplings, arXiv:1702.08016 [hep-th], 2017, p. 33.

Programs

Mathematica

t[n_, k_] := SeriesCoefficient[Sum[Binomial[n + j, j]^3 x^j, {j, 0, n + k}] (1 - x)^(3n + 1), {x, 0, k}];
a[n_] := t[2n, 2n - 1];
Array[a, 13] (* Jean-François Alcover, Feb 14 2019 *)

Sage

def a(n) :
    R. = QQ[]; p = 2*n; q = 2*n-1
    return ((1-x)^(3*p+1) * sum(binomial(p+r,r)^3 * x^r for r in [0..p+q]))[q]