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A198946 G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^n * A(x)^k] * x^n/n ). 1

%I #5 Mar 30 2012 18:37:32

%S 1,2,7,43,661,45503,14835966,19030289368,96523753164218,

%T 1826134533496656481,136782939777235335759015,

%U 38134547664565961218637677016,42464787999263932204904982967955033,176203582974534986934299369142808689004350

%N G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^n * A(x)^k] * x^n/n ).

%e G.f.: A(x) = 1 + 2*x + 7*x^2 + 43*x^3 + 661*x^4 + 45503*x^5 +...

%e where

%e log(A(x)) = (1 + A(x))*x + (1 + 2^2*A(x) + A(x)^2)*x^2/2 +

%e (1 + 3^3*A(x) + 3^3*A(x)^2 + A(x)^3)*x^3/3 +

%e (1 + 4^4*A(x) + 6^4*A(x)^2 + 4^4*A(x)^3 + A(x)^4)*x^4/4 +

%e (1 + 5^5*A(x) + 10^5*A(x)^2 + 10^5*A(x)^3 + 5^5*A(x)^4 + A(x)^5)*x^5/5 +...

%e more explicitly,

%e log(A(x)) = 2*x + 10*x^2/2 + 95*x^3/3 + 2298*x^4/4 + 220502*x^5/5 + 88457005*x^6/6 +...

%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(j=0, m, binomial(m, j)^m*(A+x*O(x^n))^j)*x^m/m))); polcoeff(A, n, x)}

%Y Cf. A198945.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 31 2011

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Last modified March 28 16:11 EDT 2024. Contains 371254 sequences. (Running on oeis4.)