A337727 a(n) = (4*n)! * Sum_{k=0..n} 1 / (4*k)!.

1, 25, 42001, 498971881, 21795091762081, 2534333270094778681, 646315807872650838343345, 317599587988620621961919733001, 274101148417699141578015206369183041, 387502275541069630431671657548241448722521, 849931991080760484603611346800010863970028660561

Offset: 0

Author

Ilya Gutkovskiy, Sep 17 2020

Keywords

• nonn

Crossrefs

Cf. A000522, A051396, A051397, A087350, A100733, A330045, A332890, A337725, A337726, A337728, A337729, A337730.

Programs

Mathematica

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

PARI

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

Formula

E.g.f.: (1/2) * (cos(x) + cosh(x)) / (1 - x^4) = 1 + 25*x^4/4! + 42001*x^8/8! + 498971881*x^12/12! + ...

a(n) = floor(c * (4*n)!), where c = (cos(1) + cosh(1)) / 2 = A332890.