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

0,4

Links

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

Formula

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).

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A087208, A182386, A337750, A337751.

Sequence in context: A309532 A123646 A123622 * A117340 A304348 A305912

Adjacent sequences: A337746 A337747 A337748 * A337750 A337751 A337752

Keyword

sign

Author

Ilya Gutkovskiy, Sep 18 2020

Status

approved