A140051 L.g.f.: A(x) = log(G(x)) where G(x) = g.f. of A060690(n) = C(2^n+n-1,n).

2, 16, 308, 14488, 1843232, 714580528, 917085102992, 4076698622618144, 64300718807613519968, 3649606003781552269341376, 752497581806524062754828125952, 567745591696108934746387351412913664

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 + 16*x^2/2 + 308*x^3/3 + 14488*x^4/4 + 1843232*x^5/5 +...
A(x) = log(G(x)) where G(x) = g.f. of A060690:
G(x) = 1 + 2*x + 10*x^2 + 120*x^3 + 3876*x^4 +... + C(2^n+n-1,n)*x^n +...

Prog

(PARI) {a(n)=n*polcoeff(log(sum(k=0, n, binomial(2^k+k-1, k)*x^k)+x*O(x^n)), n)}

Crossrefs

Cf. A140050, A060690.

Sequence in context: A009250 A335618 A174487 * A264658 A223675 A189058

Adjacent sequences: A140048 A140049 A140050 * A140052 A140053 A140054

Keyword

nonn

Author

Paul D. Hanna, May 02 2008

Status

approved