A295167 Expansion of Product_{k>0} 1/(1 + k^k*x^k)^(1/k).

1, -1, -1, -8, -50, -557, -6949, -108928, -1957445, -40752118, -952411952, -24868752445, -715354102054, -22517233371562, -769323660770868, -28367650033120436, -1122665826004076403, -47470796466768154403, -2135792162866000922808

Offset

0,4

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1/n, g(n) = -n^n.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..387

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^n*(-1)^(n/d).

Prog

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

Crossrefs

Cf. A186633.

Sequence in context: A238841 A100310 A124963 * A195231 A162236 A215874

Adjacent sequences: A295164 A295165 A295166 * A295168 A295169 A295170

Keyword

sign

Author

Seiichi Manyama, Nov 16 2017

Status

approved