%I #16 Oct 02 2013 21:38:39
%S 1,1,7,150,6924,569726,74358042,14229990742,3774315375580,
%T 1330122245198910,602741550311798067,342138788139339603446,
%U 238146938124253555981224,199695655908033678248780110,198741234873020798204357773510,231773141251670398730627959107510
%N G.f.: Sum_{n>=1} a(n)*x^n / (1 + n*x)^(n^2) = x.
%C Compare to identity: Sum_{n>=1} n^(n-2) * x^n / (1 + n*x)^n = x.
%e G.f.: x = 1*x/(1+x) + 1*x^2/(1+2*x)^4 + 7*x^3/(1+3*x)^9 + 150*x^4/(1+4*x)^16 + 6924*x^5/(1+5*x)^25 + 569726*x^6/(1+6*x)^36 +...
%o (PARI) {a(n)=polcoeff(x-sum(k=1, n-1, a(k)*x^k/(1+k*x+x*O(x^n))^(k^2)), n)}
%o for(n=1,20,print1(a(n),", "))
%Y Cf. A177447, A082157.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Oct 02 2013