A140050 L.g.f.: A(x) = log(G(x)) where G(x) = g.f. of A014070(n) = C(2^n,n).
2, 8, 140, 6840, 988272, 447403472, 660627632240, 3275795875152672, 55865676874553471264, 3342534504414732132234688, 713146571770256922167459951616, 549740788325926349073175414573702656
Offset: 1
Keywords
Examples
A(x) = 2*x + 8*x^2/2 + 140*x^3/3 + 6840*x^4/4 + 988272*x^5/5 +... A(x) = log(G(x)) where G(x) = g.f. of A014070: G(x) = 1 + 2*x + 6*x^2 + 56*x^3 + 1820*x^4 +... + C(2^n,n)*x^n +...
Programs
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PARI
{a(n)=n*polcoeff(log(sum(k=0,n,binomial(2^k,k)*x^k)+x*O(x^n)),n)}
Formula
L.g.f.: A(x) = log[ Sum_{n>=0} log(1 + 2^n*x)^n/n! ].