A348311 a(n) = n! * Sum_{k=1..n} (-1)^k * (k-2) / (k-1)!.

0, 1, 2, 3, 20, 85, 534, 3703, 29672, 266985, 2669930, 29369131, 352429692, 4581585853, 64142202110, 962133031455, 15394128503504, 261700184559313, 4710603322067922, 89501463119290195, 1790029262385804260, 37590614510101889061, 826993519222241559782

Offset

0,3

Links

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

Formula

E.g.f.: x * (1 + x) * exp(-x) / (1 - x).

a(0) = 0; a(n) = n * (a(n-1) + (-1)^n * (n-2)).

a(n) = n * (2 * A000166(n-1) + (-1)^n).

Mathematica

Table[n! Sum[(-1)^k (k - 2)/(k - 1)!, {k, 1, n}], {n, 0, 22}]
nmax = 22; CoefficientList[Series[x (1 + x) Exp[-x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) a(n) = n!*sum(k=1, n, (-1)^k * (k-2) / (k-1)!); \\ Michel Marcus, Oct 20 2021

Crossrefs

Cf. A000166, A000240, A030297, A053817, A180189, A212291.

Sequence in context: A087301 A292122 A264417 * A066166 A007113 A052804

Adjacent sequences: A348308 A348309 A348310 * A348312 A348313 A348314

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 11 2021

Status

approved