A346291 a(0) = 1; a(n) = (1/n) * Sum_{k=2..n} (binomial(n,k) * k!)^2 * a(n-k) / k.

1, 0, 1, 4, 54, 976, 27050, 1037016, 53040344, 3494603904, 288738690552, 29267185135200, 3573720291756912, 517691602686711168, 87813773085480166608, 17246816939881695262656, 3883816372280829757142400, 994217196872849143760818176, 287129874355801742457562921344

Offset

0,4

Links

Table of n, a(n) for n=0..18.

Formula

Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( polylog(2,x) - x ).

Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( Sum_{n>=2} x^n / n^2 ).

Mathematica

a[0] = 1; a[n_] := a[n] = (1/n) Sum[(Binomial[n, k] k!)^2 a[n - k]/k, {k, 2, n}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Exp[PolyLog[2, x] - x], {x, 0, nmax}], x] Range[0, nmax]!^2

Crossrefs

Cf. A000166, A074707, A346292.

Sequence in context: A303048 A304556 A127833 * A258846 A093983 A242006

Adjacent sequences: A346288 A346289 A346290 * A346292 A346293 A346294

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 13 2021

Status

approved