A292359 E.g.f.: Product_{k>=1} (1 - x^k/k).

1, -1, -1, 1, 2, 26, -6, 414, -624, -288, -20880, 164880, -9756000, 43529760, -324404640, -4052492640, -48521410560, 1168445053440, -26858914467840, 341240066334720, -5752671815116800, 49267037136844800, -769468911734476800, 39863275492626432000

Offset: 0

Author

Seiichi Manyama, Sep 14 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..451

Crossrefs

Cf. A007838, A007841.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 - x^k/k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Sep 15 2017 *)

PARI

{a(n) = n!*polcoeff(prod(k=1, n, 1-x^k/k+x*O(x^n)), n)}

Formula

Conjecture: a(n) ~ -(-1)^n * n! / n^2. - Vaclav Kotesovec, Sep 15 2017

E.g.f.: exp(-Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*j^k)). - Ilya Gutkovskiy, May 27 2018