cp's OEIS Frontend

A140050 L.g.f.: A(x) = log(G(x)) where G(x) = g.f. of A014070(n) = C(2^n,n).

%I A140050 #2 Mar 30 2012 18:37:10
%S A140050 2,8,140,6840,988272,447403472,660627632240,3275795875152672,
%T A140050 55865676874553471264,3342534504414732132234688,
%U A140050 713146571770256922167459951616,549740788325926349073175414573702656
%N A140050 L.g.f.: A(x) = log(G(x)) where G(x) = g.f. of A014070(n) = C(2^n,n).
%F A140050 L.g.f.: A(x) = log[ Sum_{n>=0} log(1 + 2^n*x)^n/n! ].
%e A140050 A(x) = 2*x + 8*x^2/2 + 140*x^3/3 + 6840*x^4/4 + 988272*x^5/5 +...
%e A140050 A(x) = log(G(x)) where G(x) = g.f. of A014070:
%e A140050 G(x) = 1 + 2*x + 6*x^2 + 56*x^3 + 1820*x^4 +... + C(2^n,n)*x^n +...
%o A140050 (PARI) {a(n)=n*polcoeff(log(sum(k=0,n,binomial(2^k,k)*x^k)+x*O(x^n)),n)}
%Y A140050 Cf. A140051, A014070.
%K A140050 nonn
%O A140050 1,1
%A A140050 _Paul D. Hanna_, May 02 2008