A294470 -id:A294470 - cp's OEIS frontend

A294469 E.g.f.: 1/Product_{k>0} (1 - x^k/k)^k.

1, 1, 4, 18, 114, 810, 7140, 68880, 766920, 9304680, 125086080, 1814015280, 28588356720, 481128888240, 8678237087520, 166041500264640, 3371031116893440, 72153115744469760, 1627441316510929920, 38500269726897538560, 954533425718494702080

Offset: 0

Seiichi Manyama, Oct 31 2017

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..443

Cf. A007841, A181541, A294470, A294471.

nmax = 20; CoefficientList[Series[Product[1/(1-x^k/k)^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Nov 01 2017 *)

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

E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*j^(k-1))). - Ilya Gutkovskiy, Sep 12 2018

A294471 E.g.f.: 1/Product_{k>0} (1+x^k/k)^k.

Original entry on oeis.org

1, -1, 0, -6, 18, -90, 660, -3360, 47880, -293160, 4277280, -36424080, 575190000, -6745218480, 101911249440, -1628086299840, 24861230634240, -484979925830400, 7629427896330240, -176975913961566720, 3036472694482106880, -77953392499390087680

Offset: 0

Seiichi Manyama, Oct 31 2017

sign

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

Cf. A292358.

Cf. A181541, A294469, A294470.

With[{nn=30},CoefficientList[Series[1/Product[(1+x^k/k)^k,{k,nn}],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 30 2021 *)

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

cp's OEIS Frontend

A294469 E.g.f.: 1/Product_{k>0} (1 - x^k/k)^k.

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