A088222 - OEIS

%I #8 Feb 18 2017 12:06:09

%S 1,2,3,10,69,678,8496,128316,2258262,45292494,1018882779,25399668480,

%T 694999352141,20710476430548,667708554093132,23159551588872624,

%U 860001996926543616,34043670528120810846,1431191816223150995395

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

%H Vaclav Kotesovec, <a href="/A088222/b088222.txt">Table of n, a(n) for n = 0..320</a>

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

%o (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)}

%o for(n=0, 20, print1(a(n), ", ")) \\ _Vaclav Kotesovec_, Feb 11 2015

%K nonn

%O 0,2

%A _Michael Somos_, Sep 24 2003