A336196 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^4 * a(k).

1, 1, 17, 1459, 395793, 262131251, 359993423843, 915919888063853, 3975467425523532305, 27639424688447366285203, 292886774320942590679779267, 4544030770812055230064359134573, 99847457331663057820508375752459491, 3021907600842518917755426740899056448141

Offset: 0

Author

Ilya Gutkovskiy, Jul 11 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..143

Crossrefs

Column k=4 of A326322.

Cf. A000670, A102221, A336195, A336197.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^4 a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]
nmax = 13; CoefficientList[Series[1/(1 - Sum[x^k/(k!)^4, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!^4

Formula

a(n) = (n!)^4 * [x^n] 1 / (1 - Sum_{k>=1} x^k / (k!)^4).