A294465 Expansion of e.g.f. Product_{k>0} (1+k*x^k)^(-1/k).
1, -1, 0, -6, 36, -180, 720, -7560, 236880, -3099600, 15120000, -194594400, 9989179200, -131935003200, 337815878400, -50154760656000, 2018231927712000, -27611162875296000, 363290246871552000, -12648028196067264000, 521752941995725440000
Offset: 0
Keywords
Programs
-
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1+k*x^k)^(1/k))))
Formula
E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^k*j^(k-1)*x^(j*k)/k). - Ilya Gutkovskiy, May 28 2018
a(0) = 1 and a(n) = -(n-1)! * Sum_{k=1..n} A076717(k)*a(n-k)/(n-k)! for n > 0. - Seiichi Manyama, Jan 21 2025