A337751 a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k / (n-4*k)!.

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

Seiichi Manyama, Table of n, a(n) for n = 0..450

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

Cf. A182386, A330045, A337749, A337750.

Sequence in context: A303411 A069756 A351905 * A362339 A358063 A367722

Adjacent sequences: A337748 A337749 A337750 * A337752 A337753 A337754

Keyword

sign

Author

Ilya Gutkovskiy, Sep 18 2020

Status

approved