|
%I #25 Dec 02 2021 19:48:04
%S 1,1,5,49,793,19361,672061,31721425,1963804529,154746407233,
%T 15136503333301,1799712380844401,255578390749947145,
%U 42713809784784354529,8296411053128532892013,1852797862395580239567121,471358206112272764630500321,135500644700064476406317390465
%N E.g.f.: exp(Sum_{n>=1} n!*x^n).
%H Seiichi Manyama, <a href="/A293847/b293847.txt">Table of n, a(n) for n = 0..253</a>
%F a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} k*k!*a(n-k)/(n-k)! for n > 0.
%F a(n) ~ n!^2. - _Vaclav Kotesovec_, Oct 18 2017
%p a:= proc(n) option remember; `if`(n=0, 1, add(
%p a(n-i)*binomial(n-1, i-1)*i!^2, i=1..n))
%p end:
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Dec 02 2021
%t nmax = 20; CoefficientList[Series[E^Sum[k!*x^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Oct 18 2017 *)
%o (PARI) {a(n) = n!*polcoeff(exp(sum(k=1, n, k!*x^k)+x*O(x^n)), n)}
%Y Cf. A158876, A159476.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 17 2017
|
