A319219 Expansion of e.g.f. Product_{k>=1} 1/(1 + x^k/(k - 1)!).

1, -1, 0, -3, 32, -105, 204, -3325, 52408, -376425, 1304180, -25766301, 659066484, -6675505837, 30765540974, -893416597515, 29169795361424, -380344619169729, 2379504317523300, -84225906785770525, 3388223174832010540, -55107296201168047221, 422923168260105913070

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*(-(j - 1)!)^k)).

Maple

seq(n!*coeff(series(mul(1/(1 + x^k/(k - 1)!), k=1..100), x=0, 23), x, n), n=0..22); # Paolo P. Lava, Jan 09 2019

Mathematica

nmax = 22; CoefficientList[Series[Product[1/(1 + x^k/(k - 1)!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 22; CoefficientList[Series[Exp[Sum[Sum[x^(j k)/(k (-(j - 1)!)^k), {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, (n - 1)! Sum[Sum[d (-(d - 1)!)^(-k/d), {d, Divisors[k]}] a[n - k]/(n - k)!, {k, 1, n}]]; Table[a[n], {n, 0, 22}]

Crossrefs

Cf. A032299, A076900, A076901, A292308, A319218.

Sequence in context: A114257 A197524 A107465 * A345687 A211224 A213845

Adjacent sequences: A319216 A319217 A319218 * A319220 A319221 A319222

Keyword

sign

Author

Ilya Gutkovskiy, Sep 13 2018

Status

approved