A088222 Coefficient of x^n in g.f.^n is A004123(n).

1, 2, 3, 10, 69, 678, 8496, 128316, 2258262, 45292494, 1018882779, 25399668480, 694999352141, 20710476430548, 667708554093132, 23159551588872624, 860001996926543616, 34043670528120810846, 1431191816223150995395

Offset: 0

Author

Michael Somos, Sep 24 2003

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..320

Programs

PARI

{a(n)=polcoeff(x/serreverse(x*exp(sum(m=1, n+1, sum(k=0, m, stirling(m, k, 2)*(2^k)*k!)*x^m/m +x^2*O(x^n)))), n)}
for(n=0, 20, print1(a(n), ", ")) \\ Vaclav Kotesovec, Feb 11 2015

Formula

a(n) ~ 4 * (n-1)! / (27 * (log(3/2))^(n+1)). - Vaclav Kotesovec, Feb 11 2015, updated Feb 18 2017