A337730 a(n) = (4*n+3)! * Sum_{k=0..n} 1 / (4*k+3)!.

1, 841, 6660721, 218205219961, 20298322381652065, 4313799472548696853801, 1816972337837511114820981201, 1372104830641374893468212163747161, 1724241814377177346127894133451232399041, 3403694723384093133512770088891935585284510985

Offset

0,2

Links

Table of n, a(n) for n=0..9.

Formula

E.g.f.: (1/2) * (sinh(x) - sin(x)) / (1 - x^4) = x^3/3! + 841*x^7/7! + 6660721*x^11/11! + 218205219961*x^15/15! + ...

a(n) = floor(c * (4*n+3)!), where c = (sinh(1) - sin(1)) / 2 = A334365.

Mathematica

Table[(4 n + 3)! Sum[1/(4 k + 3)!, {k, 0, n}], {n, 0, 9}]
Table[(4 n + 3)! SeriesCoefficient[(1/2) (Sinh[x] - Sin[x])/(1 - x^4), {x, 0, 4 n + 3}], {n, 0, 9}]
Table[Floor[(1/2) (Sinh[1] - Sin[1]) (4 n + 3)!], {n, 0, 9}]

Prog

(PARI) a(n) = (4*n+3)!*sum(k=0, n, 1/(4*k+3)!); \\ Michel Marcus, Sep 17 2020

Crossrefs

Cf. A000522, A051396, A051397, A087350, A330045, A334365, A337725, A337726, A337727, A337728, A337729.

Sequence in context: A121499 A253514 A342841 * A049530 A158404 A004929

Adjacent sequences: A337727 A337728 A337729 * A337731 A337732 A337733

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 17 2020

Status

approved