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A337751
a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k / (n-4*k)!.
3
1, 1, 1, 1, -23, -119, -359, -839, 38641, 359857, 1809361, 6644881, -459055079, -6175146119, -43468088663, -217686301559, 20051525850721, 352724346317281, 3192296431410721, 20250050516224417, -2331591425921837879, -50665325105014242839, -560439561498466178759
OFFSET
0,5
LINKS
FORMULA
G.f.: Sum_{k>=0} (-1)^k * (4*k)! * x^(4*k) / (1 - x)^(4*k+1).
E.g.f.: exp(x) / (1 + x^4).
a(0) = a(1) = a(2) = a(3) = 1; a(n) = 1 - n * (n-1) * (n-2) * (n-3) * a(n-4).
MATHEMATICA
Table[n! Sum[(-1)^k/(n - 4 k)!, {k, 0, Floor[n/4]}], {n, 0, 22}]
nmax = 22; CoefficientList[Series[Exp[x]/(1 + x^4), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) a(n) = n!*sum(k=0, n\4, (-1)^k / (n-4*k)!); \\ Michel Marcus, Sep 18 2020
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Sep 18 2020
STATUS
approved