A319218 Expansion of e.g.f. Product_{k>=1} (1 - x^k/(k - 1)!).

1, -1, -2, 3, 8, 75, -216, -175, -3816, -36225, 189800, 325149, 2375460, 25547951, 386162126, -3290670825, -6316583056, -59290501809, -310987223208, -4836373835707, -86500419684420, 1119358992256239, 3043733432729198, 26408738842522959, 169835931388147464

Offset

0,3

Links

Table of n, a(n) for n=0..24.

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 - x^k/(k - 1)!), k=1..100), x=0, 25), x, n), n=0..24); # Paolo P. Lava, Jan 09 2019

Mathematica

nmax = 24; CoefficientList[Series[Product[(1 - x^k/(k - 1)!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 24; 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, 24}]

Crossrefs

Cf. A032299, A076900, A185895, A319219.

Sequence in context: A354574 A042815 A191353 * A358562 A368246 A243954

Adjacent sequences: A319215 A319216 A319217 * A319219 A319220 A319221

Keyword

sign

Author

Ilya Gutkovskiy, Sep 13 2018

Status

approved