A229806 G.f.: Sum_{n>=1} a(n)*x^n / (1 + n*x)^(n^2) = x.

1, 1, 7, 150, 6924, 569726, 74358042, 14229990742, 3774315375580, 1330122245198910, 602741550311798067, 342138788139339603446, 238146938124253555981224, 199695655908033678248780110, 198741234873020798204357773510, 231773141251670398730627959107510

Offset: 1

Author

Paul D. Hanna, Oct 02 2013

Keywords

• nonn

Comments

Compare to identity: Sum_{n>=1} n^(n-2) * x^n / (1 + n*x)^n = x.

Examples

			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 +...
		

Crossrefs

Cf. A177447, A082157.

Programs

PARI

{a(n)=polcoeff(x-sum(k=1, n-1, a(k)*x^k/(1+k*x+x*O(x^n))^(k^2)), n)}
for(n=1,20,print1(a(n),", "))