OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..450
FORMULA
G.f.: Sum_{k>=0} (4*k)! * x^(4*k) / (1 - x)^(4*k + 1).
a(0) = a(1) = a(2) = a(3) = 1; a(n) = n*(n - 1)*(n - 2)*(n - 3)*a(n - 4) + 1.
a(n) = Sum_{k=0..floor(n/4)} n! / (n - 4*k)!.
a(n) ~ n! * (2*cos(Pi*n/2 - 1) + exp(1) + (-1)^n*exp(-1))/4. - Vaclav Kotesovec, Apr 18 2020
MATHEMATICA
nmax = 22; CoefficientList[Series[Exp[x]/(1 - x^4), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[n!/(n - 4 k)!, {k, 0, Floor[n/4]}], {n, 0, 22}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 28 2019
STATUS
approved