A346292 a(0) = 1; a(n) = (1/n) * Sum_{k=3..n} (binomial(n,k) * k!)^2 * a(n-k) / k.

1, 0, 0, 4, 36, 576, 17600, 694800, 35802144, 2391438336, 200018045952, 20476348214400, 2521840589347200, 368057828019898368, 62841061478699292672, 12413136137144581203456, 2809529229255558769612800, 722458985698006017844838400, 209487621780682072569567903744

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 - x^2 / 4 ).

Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( Sum_{n>=3} 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, 3, n}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Exp[PolyLog[2, x] - x - x^2/4], {x, 0, nmax}], x] Range[0, nmax]!^2

Crossrefs

Cf. A038205, A074707, A346291.

Sequence in context: A001044 A306736 A307845 * A086879 A372241 A363010

Adjacent sequences: A346289 A346290 A346291 * A346293 A346294 A346295

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 13 2021

Status

approved