A349087 -id:A349087 - cp's OEIS frontend

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

Ilya Gutkovskiy, Mar 25 2022

nonn

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

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

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]!

a(n) = n! * sum(k=0, n\4, 1/(4*k)!); \\ Michel Marcus, Mar 29 2022

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

a(n) = floor(c * n!), where c = 1.04169147... = A332890.

A348597 a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k / (3*k)!.

Original entry on oeis.org

1, 1, 2, 5, 20, 100, 601, 4207, 33656, 302903, 3029030, 33319330, 399831961, 5197815493, 72769416902, 1091541253529, 17464660056464, 296899220959888, 5344185977277985, 101539533568281715, 2030790671365634300, 42646604098678320299, 938225290170923046578

Offset: 0

Ilya Gutkovskiy, Mar 25 2022

nonn

Cf. A000166, A009102, A346441, A349087, A352659.

Table[n! Sum[(-1)^k/(3 k)!, {k, 0, Floor[n/3]}], {n, 0, 22}]
nmax = 22; CoefficientList[Series[(Exp[-x] + 2 Exp[x/2] Cos[Sqrt[3] x/2])/(3 (1 - x)), {x, 0, nmax}], x] Range[0, nmax]!

E.g.f.: (exp(-x) + 2 * exp(x/2) * cos(sqrt(3)*x/2)) / (3*(1 - x)).

a(n) = round(c * n!), where c = 0.834719468... = A346441.

cp's OEIS Frontend

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

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