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A330044 Expansion of e.g.f. exp(x) / (1 - x^3). 5
1, 1, 1, 7, 25, 61, 841, 5251, 20497, 423865, 3780721, 20292031, 559501801, 6487717237, 44317795705, 1527439916731, 21798729916321, 180816606476401, 7478345832314977, 126737815733490295, 1236785588298582841, 59677199741873516461, 1171057417377450325801 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

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

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

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

a(n) ~ n! * (exp(1)/3 + 2*cos(sqrt(3)/2 - 2*Pi*n/3) / (3*exp(1/2))). - Vaclav Kotesovec, Apr 18 2020

MATHEMATICA

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

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

CROSSREFS

Cf. A000522, A087208, A100732, A330045.

Sequence in context: A321165 A118395 A118396 * A193375 A185787 A299273

Adjacent sequences:  A330041 A330042 A330043 * A330045 A330046 A330047

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 28 2019

STATUS

approved

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Last modified February 24 18:55 EST 2021. Contains 341584 sequences. (Running on oeis4.)