A192204 - OEIS

%I #5 Mar 30 2012 18:37:27

%S 1,2,13,109,1099,12283,147620,1869346,24633344,334916467,4669887745,

%T 66481991644,963096090267,14160279233964,210870471771803,

%U 3175275874056722,48281516978747396,740504452581897112,11444972742343813815

%N G.f.: A(x) = exp( Sum_{n>=1} (Sum_{k=0..n} C(n,k)^4*A(x)^k) * x^n/n ).

%e G.f.: A(x) = 1 + 2*x + 13*x^2 + 109*x^3 + 1099*x^4 + 12283*x^5 +...

%e which satisfies:

%e log(A(x)) = (1 + A(x))*x + (1 + 16*A(x) + A(x)^2)*x^2/2 + (1 + 81*A(x) + 81*A(x)^2 + A(x)^3)*x^3/3 + (1 + 256*A(x) + 1296*A(x)^2 + 256*A(x)^3 + A(x)^4)*x^4/4 +...

%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)^4*(A+x*O(x^n))^j)*x^m/m))); polcoeff(A, n, x)}

%Y Cf. variants: A007863, A192131.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 25 2011