A337730 - OEIS

%I #8 Sep 17 2020 20:31:52

%S 1,841,6660721,218205219961,20298322381652065,4313799472548696853801,

%T 1816972337837511114820981201,1372104830641374893468212163747161,

%U 1724241814377177346127894133451232399041,3403694723384093133512770088891935585284510985

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

%F 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! + ...

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

%t Table[(4 n + 3)! Sum[1/(4 k + 3)!, {k, 0, n}], {n, 0, 9}]

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

%t Table[Floor[(1/2) (Sinh[1] - Sin[1]) (4 n + 3)!], {n, 0, 9}]

%o (PARI) a(n) = (4*n+3)!*sum(k=0, n, 1/(4*k+3)!); \\ _Michel Marcus_, Sep 17 2020

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

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Sep 17 2020