A156911 G.f.: A(x) = exp( Sum_{n>=1} 3^(n^2)/(1 - 3^n*x)^n * x^n/n ).

1, 3, 54, 7470, 11326446, 173007630594, 25222890606413004, 34295263336258106333292, 429734207324188407742780371030, 49292144072318945019920850119049478578

Offset

0,2

Comments

An example of this logarithmic identity at q=3:

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..9.

Formula

G.f.: A(x) = (1-x)*exp( Sum_{n>=1} (1 + 3^n)^n * x^n/n );

Equals the first differences of A155204.

Example

G.f.: A(x) = 1 + 3*x + 54*x^2 + 7470*x^3 + 11326446*x^4 +...
Log(A(x)) = 3/(1-3*x)*x + 3^4/(1-3^2*x)^2*x^2/2 + 3^9/(1-3^3*x)^3*x^3/3 +...
Log(A(x)) = (4-1)*x + (10^2-1)*x^2/2 + (28^3-1)*x^3/3 + (82^4-1)*x^4/4 +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, 3^(m^2)/(1-3^m*x)^m*x^m/m)+x*O(x^n)), n)}
(PARI) /* As First Differences of A155204: */
{a(n)=polcoeff((1-x)*exp(sum(m=1, n+1, (3^m+1)^m*x^m/m)+x*O(x^n)), n)}

Crossrefs

Cf. A155204, A155203, A155205, A156910.

Sequence in context: A174579 A171739 A157568 * A214006 A154604 A188798

Adjacent sequences: A156908 A156909 A156910 * A156912 A156913 A156914

Keyword

nonn

Author

Paul D. Hanna, Feb 17 2009

Status

approved