A292358 E.g.f.: Product_{k>=1} 1/(1 + x^k/k).

1, -1, 1, -5, 20, -104, 584, -4304, 35720, -329160, 3239112, -36135912, 438454752, -5743527360, 80351263680, -1218698312064, 19599583392384, -334335747652224, 6019295318075520, -114911886106373760, 2305234779285164544, -48596575400453366784

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..449

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A007838, A007841.

Sequence in context: A092640 A165961 A276314 * A259275 A109500 A137961

Adjacent sequences: A292355 A292356 A292357 * A292359 A292360 A292361

Keyword

sign

Author

Seiichi Manyama, Sep 14 2017

Status

approved