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
Keywords
Examples
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 +...
Programs
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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)}
Formula
G.f.: A(x) = (1-x)*exp( Sum_{n>=1} (1 + 3^n)^n * x^n/n );
Equals the first differences of A155204.
Comments