A155209 G.f.: A(x) = exp( Sum_{n>=1} (4^n - 1)^n * x^n/n ), a power series in x with integer coefficients.

1, 3, 117, 83691, 1057319541, 224085796087563, 785909534807110163445, 45253898808490419883694669835, 42530103981310660908750359650219091445, 649533982980850199063905669772208004250784346635

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.

Example

G.f.: A(x) = 1 + 3*x + 117*x^2 + 83691*x^3 + 1057319541*x^4 +...
log(A(x)) = 3*x + 15^2*x^2/2 + 63^3*x^3/3 + 255^4*x^4/4 + 1023^5*x^5/5 +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (4^m-1)^m*x^m/m)+x*O(x^n)), n)}

Crossrefs

Cf. A155207, A155208, A155210, variants: A155202, A155205.

Sequence in context: A097642 A009095 A326995 * A037117 A283883 A173053

Adjacent sequences: A155206 A155207 A155208 * A155210 A155211 A155212

Keyword

nonn

Author

Paul D. Hanna, Feb 04 2009

Status

approved