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A352660
a(n) = n! * Sum_{k=0..floor(n/4)} 1 / (4*k)!.
4
1, 1, 2, 6, 25, 125, 750, 5250, 42001, 378009, 3780090, 41580990, 498971881, 6486634453, 90812882342, 1362193235130, 21795091762081, 370516559955377, 6669298079196786, 126716663504738934, 2534333270094778681, 53220998671990352301, 1170861970783787750622
OFFSET
0,3
LINKS
FORMULA
E.g.f.: (cos(x) + cosh(x)) / (2*(1 - x)).
a(n) = floor(c * n!), where c = 1.04169147... = A332890.
MATHEMATICA
Table[n! Sum[1/(4 k)!, {k, 0, Floor[n/4]}], {n, 0, 22}]
nmax = 22; CoefficientList[Series[(Cos[x] + Cosh[x])/(2 (1 - x)), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) a(n) = n! * sum(k=0, n\4, 1/(4*k)!); \\ Michel Marcus, Mar 29 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 25 2022
STATUS
approved