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A156910 G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)/(1 - 2^n*x)^n * x^n/n ). 1
1, 2, 14, 268, 21462, 7872396, 12585797612, 84949155244024, 2379063526056509734, 273414369715003663482380, 128009001272184822673783879332, 242979321424122460096958142064785384 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

An example of this logarithmic identity at q=2:

Sum_{n>=1} [q^(n^2)/(1 - q^n*x)^n]*x^n/n = Sum_{n>=1} [(1 + q^n)^n - 1]*x^n/n.

LINKS

Table of n, a(n) for n=0..11.

FORMULA

G.f.: A(x) = (1-x)*exp( Sum_{n>=1} (1 + 2^n)^n * x^n/n );

Equals the first differences of A155201.

EXAMPLE

G.f.: A(x) = 1 + 2*x + 14*x^2 + 268*x^3 + 21462*x^4 +...

log(A(x)) = 2/(1-2*x)*x + 2^4/(1-2^2*x)^2*x^2/2 + 2^9/(1-2^3*x)^3*x^3/3 +...

log(A(x)) = (3-1)*x + (5^2-1)*x^2/2 + (9^3-1)*x^3/3 + (17^4-1)*x^4/4 +...

PROG

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

(PARI) /* As First Differences of A155201: */

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

CROSSREFS

Cf. A155201, A155200.

Sequence in context: A187654 A280517 A015197 * A279117 A018803 A217474

Adjacent sequences:  A156907 A156908 A156909 * A156911 A156912 A156913

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 17 2009

STATUS

approved

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Last modified September 23 12:43 EDT 2021. Contains 347617 sequences. (Running on oeis4.)