cp's OEIS Frontend

A156630 G.f.: A(x) = Sum_{n>=0} [ Sum_{k>=1} (2^n + 2^k)^k*x^k/k ]^n / n!, a power series in x with integer coefficients.

%I A156630 #2 Mar 30 2012 18:37:16
%S A156630 1,4,36,692,38186,10012732,14013453284,89892733239928,
%T A156630 2455110210935634790,278266942487534934333100,
%U A156630 129264916198375365693754194988,244287539590735476133066282560012360
%N A156630 G.f.: A(x) = Sum_{n>=0} [ Sum_{k>=1} (2^n + 2^k)^k*x^k/k ]^n / n!, a power series in x with integer coefficients.
%C A156630 Compare to these dual g.f.s:
%C A156630 Sum_{n>=0} [ Sum_{k>=1} (2^n+1)^k*x^k/k ]^n/n! (A133991);
%C A156630 Sum_{n>=0} [ Sum_{k>=1} (2^k+1)^k*x^k/k ]^n/n! (A155201);
%C A156630 which, when expanded as power series in x, have only integer coefficients.
%e A156630 G.f.: A(x) = 1 + 4*x + 36*x^2 + 692*x^3 + 38186*x^4 + 10012732*x^5 +...
%o A156630 (PARI) {a(n)=polcoeff(sum(j=0,n,sum(k=1, n, ((2^j+2^k)*x)^k/k+x*O(x^n))^j/j!),n)}
%Y A156630 Cf. A156631, A133991, A155201.
%K A156630 nonn
%O A156630 0,2
%A A156630 _Paul D. Hanna_, Feb 12 2009