OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..450
FORMULA
a(n) ~ n! * (1 - 1/n - 1/n^2 - 4/n^3 - 23/n^4 - 171/n^5 - 1542/n^6 - 16241/n^7 - 194973/n^8 - 2622610/n^9 - 39027573/n^10 - ...), for coefficients see A113869. - Vaclav Kotesovec, Jun 18 2019
MAPLE
A158094:= proc(n)
option remember;
local S;
S:= series(add(k!*x^k, k=0..n)/mul(1+A158094(k)*x^k, k=1..n-1), x, n+1);
coeff(S, x, n)
end; # Robert Israel, Mar 04 2014
MATHEMATICA
a[n_] := a[n] = Module[{s}, s = Series[Sum[k!*x^k, {k, 0, n}]/Product[1+a[k]*x^k, {k, 1, n-1}], {x, 0, n+1}]; Coefficient[s, x, n]]; Table[a[n], {n, 1, 20}] (* Jean-François Alcover, Mar 04 2014, after Maple *)
PROG
(PARI) {a(n)=if(n<1, 0, polcoeff(sum(k=0, n, k!*x^k)/prod(k=1, n-1, 1+a(k)*x^k +x*O(x^n)), n))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 15 2009
STATUS
approved