A293847 E.g.f.: exp(Sum_{n>=1} n!*x^n).

1, 1, 5, 49, 793, 19361, 672061, 31721425, 1963804529, 154746407233, 15136503333301, 1799712380844401, 255578390749947145, 42713809784784354529, 8296411053128532892013, 1852797862395580239567121, 471358206112272764630500321, 135500644700064476406317390465

Offset: 0

Author

Seiichi Manyama, Oct 17 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..253

Crossrefs

Cf. A158876, A159476.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-i)*binomial(n-1, i-1)*i!^2, i=1..n))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Dec 02 2021

Mathematica

nmax = 20; CoefficientList[Series[E^Sum[k!*x^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 18 2017 *)

PARI

{a(n) = n!*polcoeff(exp(sum(k=1, n, k!*x^k)+x*O(x^n)), n)}

Formula

a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} k*k!*a(n-k)/(n-k)! for n > 0.

a(n) ~ n!^2. - Vaclav Kotesovec, Oct 18 2017