A136553 G.f.: A(x) = Sum_{n>=0} log( Sum_{k>=0} (k+1)^n*x^k )^n / n!.

1, 2, 9, 90, 2577, 248236, 84052116, 100270156156, 421825834327399, 6296015371464642774, 336474161890278633077823, 65028162589779857302801760924, 45874159173058581016227457835479612

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Example

G.f.: A(x) = 1 + 2*x + 9*x^2 + 90*x^3 + 2577*x^4 + 248236*x^5 +...;
A(x) = Sum_{n>=0} log(1 + 2^n*x + 3^n*x^2 + 4^n*x^3 +...)^n / n! ; surprisingly, this sum yields a series in x with integer coefficients.

Prog

(PARI) {a(n)=polcoeff(sum(i=0, n, log(sum(k=0, n, (k+1)^i*x^k)+x*O(x^n))^i/i!), n)}

Crossrefs

Cf. A136552.

Sequence in context: A012941 A216691 A059477 * A266293 A368840 A224323

Adjacent sequences: A136550 A136551 A136552 * A136554 A136555 A136556

Keyword

nonn

Author

Paul D. Hanna, Jan 05 2008

Status

approved