A295244 Expansion of Product_{k>=1} (1 + k^k*x^k)^k.

1, 1, 8, 89, 1121, 17313, 306588, 6264356, 144123978, 3710660797, 105517536463, 3289885612007, 111534718552758, 4086488012360688, 160872398645645560, 6772203940050042913, 303547711924399057195, 14433006933542826499824

Offset: 0

Author

Seiichi Manyama, Nov 18 2017

Keywords

• nonn

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -n, g(n) = -n^n.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..385

Crossrefs

Cf. A266964, A294809, A295245.

Programs

PARI

N=66; x='x+O('x^N); Vec(prod(k=1, N, (1+k^k*x^k)^k))

Formula

a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} b(k)*a(n-k) where b(n) = Sum_{d|n} d^(2+n)*(-1)^(1+n/d).