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A155205 G.f.: A(x) = exp( Sum_{n>=1} (3^n - 1)^n * x^n/n ), a power series in x with integer coefficients. 6
1, 2, 34, 5924, 10252294, 166020197708, 24810918565918804, 34076399079565985138408, 428687477154543524080261047622, 49247086840315416213775472777558582540 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

LINKS

Table of n, a(n) for n=0..9.

EXAMPLE

G.f.: A(x) = 1 + 2*x + 34*x^2 + 5924*x^3 + 10252294*x^4 +...

log(A(x)) = 2*x + 8^2*x^2/2 + 26^3*x^3/3 + 80^4*x^4/4 + 242^5*x^5/5 +...

PROG

(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (3^m-1)^m*x^m/m)+x*O(x^n)), n)}

CROSSREFS

Cf. A155203, A155204, A155206, A155812 (triangle), variants: A155202, A155209.

Sequence in context: A206501 A183414 A002782 * A303444 A230244 A045529

Adjacent sequences:  A155202 A155203 A155204 * A155206 A155207 A155208

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 04 2009

STATUS

approved

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Last modified November 21 09:14 EST 2019. Contains 329362 sequences. (Running on oeis4.)