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A348311
a(n) = n! * Sum_{k=1..n} (-1)^k * (k-2) / (k-1)!.
0
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 11 2021
STATUS
approved