A336243 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * (n-k-1)! * a(k).

1, 1, 5, 56, 1114, 34624, 1549648, 94402356, 7511324448, 756406501200, 94039208461584, 14146468841290752, 2532586289913605088, 532113978869395649856, 129662518122880634567232, 36270261084908437106586624, 11543682123659880166705099776

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = (n!)^2 * [x^n] 1 / (1 - Sum_{k>=1} x^k / (k*k!)).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^2 (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; CoefficientList[Series[1/(1 - Sum[x^k/(k k!), {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!^2
nmax = 16; Assuming[x > 0, CoefficientList[Series[1/(1 + EulerGamma - ExpIntegralEi[x] + Log[x]), {x, 0, nmax}], x]] Range[0, nmax]!^2

Crossrefs

Cf. A007840, A102221, A110083, A193161.

Sequence in context: A060080 A203522 A180874 * A356134 A363059 A163793

Adjacent sequences: A336240 A336241 A336242 * A336244 A336245 A336246

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 13 2020

Status

approved