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

1,1

Links

Table of n, a(n) for n=1..12.

Formula

L.g.f.: A(x) = log[ Sum_{n>=0} log(1 + 2^n*x)^n/n! ].

Example

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 +...

Prog

(PARI) {a(n)=n*polcoeff(log(sum(k=0, n, binomial(2^k, k)*x^k)+x*O(x^n)), n)}

Crossrefs

Cf. A140051, A014070.

Sequence in context: A045330 A193203 A259126 * A318038 A304798 A154908

Adjacent sequences: A140047 A140048 A140049 * A140051 A140052 A140053

Keyword

nonn

Author

Paul D. Hanna, May 02 2008

Status

approved