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 A229806 G.f.: Sum_{n>=1} a(n)*x^n / (1 + n*x)^(n^2) = x. 0

%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

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Last modified December 7 01:11 EST 2023. Contains 367616 sequences. (Running on oeis4.)