A336195 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^3 * a(k).

1, 1, 9, 271, 19353, 2699251, 650553183, 248978967973, 142238892608025, 115699539306013867, 129097362200437841259, 191726066802105786953113, 369666963359241578736653775, 906204961889202975320635813201, 2774573804997927027583123365125685

Offset: 0

Author

Ilya Gutkovskiy, Jul 11 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..180

Crossrefs

Column k=3 of A326322.

Cf. A000670, A102221, A336196, A336197.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^3 a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 14}]
nmax = 14; CoefficientList[Series[1/(1 - Sum[x^k/(k!)^3, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!^3

Formula

a(n) = (n!)^3 * [x^n] 1 / (1 - Sum_{k>=1} x^k / (k!)^3).