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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
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.
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 A365881
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 04 2009
STATUS
approved