A337728 a(n) = (4*n+1)! * Sum_{k=0..n} 1 / (4*k+1)!.

1, 121, 365905, 6278929801, 358652470233121, 51516840824285500441, 15640512874253077933887601, 8915467710633236496186345872425, 8755702529258688898174686554391144001, 13878488965077362598718732163634314533105081, 33731389859841228248933904149069928786421237268881

Offset

0,2

Links

Table of n, a(n) for n=0..10.

Formula

E.g.f.: (1/2) * (sin(x) + sinh(x)) / (1 - x^4) = x + 121*x^5/5! + 365905*x^9/9! + 6278929801*x^13/13! + ...

a(n) = floor(c * (4*n+1)!), where c = (sin(1) + sinh(1)) / 2 = A334363.

Mathematica

Table[(4 n + 1)! Sum[1/(4 k + 1)!, {k, 0, n}], {n, 0, 10}]
Table[(4 n + 1)! SeriesCoefficient[(1/2) (Sin[x] + Sinh[x])/(1 - x^4), {x, 0, 4 n + 1}], {n, 0, 10}]
Table[Floor[(1/2) (Sin[1] + Sinh[1]) (4 n + 1)!], {n, 0, 10}]

Prog

(PARI) a(n) = (4*n+1)!*sum(k=0, n, 1/(4*k+1)!); \\ Michel Marcus, Sep 17 2020

Crossrefs

Cf. A000522, A051396, A051397, A087350, A330045, A334363, A337725, A337726, A337727, A337729, A337730.

Sequence in context: A178192 A135825 A221392 * A227301 A261364 A317956

Adjacent sequences: A337725 A337726 A337727 * A337729 A337730 A337731

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 17 2020

Status

approved