A337750 - OEIS

A337750

a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k / (n-3*k)!.

1, 1, 1, -5, -23, -59, 601, 4831, 19825, -302903, -3478319, -19626749, 399831961, 5968795405, 42864819817, -1091541253529, -20055152560799, -174888464853359, 5344185977277985, 116600656988485387, 1196237099596975561, -42646604098678320299, -1077390070573604975879

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OFFSET

0,4

LINKS

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

FORMULA

G.f.: Sum_{k>=0} (-1)^k * (3*k)! * x^(3*k) / (1 - x)^(3*k+1).

E.g.f.: exp(x) / (1 + x^3).

a(0) = a(1) = a(2) = 1; a(n) = 1 - n * (n-1) * (n-2) * a(n-3).

MATHEMATICA

Table[n! Sum[(-1)^k/(n - 3 k)!, {k, 0, Floor[n/3]}], {n, 0, 22}]

nmax = 22; CoefficientList[Series[Exp[x]/(1 + x^3), {x, 0, nmax}], x] Range[0, nmax]!