The On-Line Encyclopedia of Integer Sequences (OEIS)

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A155202

G.f.: A(x) = exp( Sum_{n>=1} (2^n - 1)^n * x^n/n ), a power series in x with integer coefficients.
(history; published version)

#2 by Russ Cox at Fri Mar 30 18:37:15 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Feb 04 2009

Discussion

Fri Mar 30

18:37

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

#1 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

NAME

G.f.: A(x) = exp( Sum_{n>=1} (2^n - 1)^n * x^n/n ), a power series in x with integer coefficients.

DATA

1, 1, 5, 119, 12783, 5739069, 10426379903, 76135573607705, 2234839096465512877, 263966776643953756165279, 125532809982533901346598445525, 240383033223427436734891985275952307

OFFSET

0,3

COMMENTS

More generally, for m integer, exp( Sum_{n>=1} (m^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.

EXAMPLE

G.f.: A(x) = 1 + x + 5*x^2 + 119*x^3 + 12783*x^4 + 5739069*x^5 +...

log(A(x)) = x + 3^2*x^2/2 + 7^3*x^3/3 + 15^4*x^4/4 + 31^5*x^5/5 +...

PROG

(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (2^m-1)^m*x^m/m)+x*O(x^n)), n)}

CROSSREFS

Cf. A155200, A155202, A155810 (triangle), variants: A155205, A155209.

KEYWORD

nonn,new

AUTHOR

Paul D. Hanna (pauldhanna(AT)juno.com), Feb 04 2009

STATUS

approved