A352660 a(n) = n! * Sum_{k=0..floor(n/4)} 1 / (4*k)!.

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

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

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

Cf. A000522, A009179, A332890, A337727, A349087, A352659.

Sequence in context: A370510 A370511 A074010 * A349088 A030806 A030828

Adjacent sequences: A352657 A352658 A352659 * A352661 A352662 A352663

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 25 2022

Status

approved