The On-Line Encyclopedia of Integer Sequences (OEIS)

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A140051

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

#2 by Russ Cox at Fri Mar 30 18:37:10 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, May 02 2008

Discussion

Fri Mar 30

18:37

OEIS Server: https://oeis.org/edit/global/213

#1 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

NAME

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

DATA

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

OFFSET

1,1

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.

KEYWORD

nonn

AUTHOR

Paul D. Hanna (pauldhanna(AT)juno.com), May 02 2008

STATUS

approved