A294948 Expansion of Product_{n>=1} (1 - n^n*x^n)^(1/n).

1, -1, -2, -7, -57, -541, -7126, -108072, -1966034, -40620681, -952305757, -24824933859, -714742428220, -22491627743504, -768696164146118, -28344822040761041, -1121925480573229737, -47442205907345238412, -2134679753840086267669

Offset: 0

Author

Seiichi Manyama, Nov 11 2017

Keywords

• sign

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

Crossrefs

Column k=0 of A294947.

Cf. A023881, A023887.

Programs

PARI

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

Formula

G.f.: exp(-Sum_{k>0} A023887(k)*x^k/k).

a(0) = 1 and a(n) = -(1/n) * Sum_{k=1..n} A023887(k)*a(n-k) for n > 0.