A337750 -id:A337750 - cp's OEIS frontend

A337749 a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k / (n-2*k)!.

1, 1, -1, -5, 13, 101, -389, -4241, 21785, 305353, -1960649, -33588829, 258805669, 5239857325, -47102631757, -1100370038249, 11304631621681, 299300650403729, -3459217276234385, -102360822438075317, 1314502564969066301, 42991545423991633141, -607300185015708631061

Offset: 0

Ilya Gutkovskiy, Sep 18 2020

sign

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

Cf. A087208, A182386, A337750, A337751.

Table[n! Sum[(-1)^k/(n - 2 k)!, {k, 0, Floor[n/2]}], {n, 0, 22}]
nmax = 22; CoefficientList[Series[Exp[x]/(1 + x^2), {x, 0, nmax}], x] Range[0, nmax]!
(* alternative code *)
f[x_]:=I*(ExpIntegralE[-x,I]*E^I-ExpIntegralE[-x,-I]*E^(-I))/2
FunctionExpand[Array[f,20,0]] (* Velin Yanev, Oct 13 2021 *)

a(n) = n!*sum(k=0, n\2, (-1)^k / (n-2*k)!); \\ Michel Marcus, Sep 18 2020

G.f.: Sum_{k>=0} (-1)^k * (2*k)! * x^(2*k) / (1 - x)^(2*k+1).
E.g.f.: exp(x) / (1 + x^2).
a(0) = a(1) = 1; a(n) = 1 - n * (n-1) * a(n-2).

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Sep 18 2020

sign

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

Cf. A182386, A330045, A337749, A337750.

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]!

a(n) = n!*sum(k=0, n\4, (-1)^k / (n-4*k)!); \\ Michel Marcus, Sep 18 2020

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).

cp's OEIS Frontend

A337749 a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k / (n-2*k)!.

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