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A155204 G.f.: A(x) = exp( Sum_{n>=1} (3^n + 1)^n * x^n/n ), a power series in x with integer coefficients. 7
1, 4, 58, 7528, 11333974, 173018964568, 25223063625377572, 34295288559321731710864, 429734241619476967064512081894, 49292144502053186639397817183561560472 (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.

FORMULA

Equals row sums of triangle A155812.

EXAMPLE

G.f.: A(x) = 1 + 4*x + 58*x^2 + 7528*x^3 + 11333974*x^4 + 173018964568*x^5 +...

log(A(x)) = 4*x + 10^2*x^2/2 + 28*x^3/3 + 82^4*x^4/4 + 244^5*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, A155205, A155206, A155812 (triangle), variants: A155201, A155208.

Sequence in context: A229528 A109056 A326944 * A290765 A144992 A198511

Adjacent sequences:  A155201 A155202 A155203 * A155205 A155206 A155207

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 04 2009

STATUS

approved

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Last modified April 3 20:29 EDT 2020. Contains 333199 sequences. (Running on oeis4.)