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A181076 G.f.: exp( Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^n *x^k ] *x^n/n ).

%I A181076 #2 Mar 30 2012 18:37:22
%S A181076 1,1,2,5,20,168,3659,204644,25503314,7434144333,5248999682258,
%T A181076 8079852389207554,28328874782544308254,244277149833867010587231,
%U A181076 4673118265932181394325207044,198007423467261943865049734612821
%N A181076 G.f.: exp( Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^n *x^k ] *x^n/n ).
%C A181076 Conjecture: this sequence consists entirely of integers.
%e A181076 G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 20*x^4 + 168*x^5 + 3659*x^6 +...
%e A181076 The logarithm begins:
%e A181076 log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 59*x^4/4 + 726*x^5/5 + 20832*x^6/6 +...+ A181077(n)*x^n/n +...
%e A181076 which equals the series:
%e A181076 log(A(x)) = (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 +...)*x
%e A181076 + (1 + 2^2*x + 3^2*x^2 + 4^2*x^3 + 5^2*x^4 + 6^2*x^5 +...)*x^2/2
%e A181076 + (1 + 3^3*x + 6^3*x^2 + 10^3*x^3 + 15^3*x^4 + 21^3*x^5 +...)*x^3/3
%e A181076 + (1 + 4^4*x + 10^4*x^2 + 20^4*x^3 + 35^4*x^4 + 56^4*x^5 +...)*x^4/4
%e A181076 + (1 + 5^5*x + 15^5*x^2 + 35^5*x^3 + 70^5*x^4 + 126^5*x^5 +...)*x^5/5
%e A181076 + (1 + 6^6*x + 21^6*x^2 + 56^6*x^3 + 126^6*x^4 + 252^6*x^5 +...)*x^6/6
%e A181076 + (1 + 7^7*x + 28^7*x^2 + 84^7*x^3 + 210^7*x^4 + 462^7*x^5 +...)*x^7/7 +...
%o A181076 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, n, binomial(m+k-1,k)^m*x^k)*x^m/m)+x*O(x^n)), n)}
%Y A181076 Cf. A181077 (log), variants: A181074, A181078.
%K A181076 nonn
%O A181076 0,3
%A A181076 _Paul D. Hanna_, Oct 02 2010