A349087 - OEIS

A349087

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

1, 1, 2, 6, 23, 115, 690, 4830, 38641, 347769, 3477690, 38254590, 459055079, 5967716027, 83548024378, 1253220365670, 20051525850721, 340875939462257, 6135766910320626, 116579571296091894, 2331591425921837879, 48963419944358595459, 1077195238775889100098

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

FORMULA

E.g.f.: cos(x/sqrt(2)) * cosh(x/sqrt(2)) / (1 - x).

a(n) = round(c * n!), where c = 0.9583581... = A346440.

MATHEMATICA

Table[n! Sum[(-1)^k/(4 k)!, {k, 0, Floor[n/4]}], {n, 0, 22}]

nmax = 22; CoefficientList[Series[Cos[x/Sqrt[2]] Cosh[x/Sqrt[2]]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!

CROSSREFS