A337729 - OEIS

%I #8 Sep 17 2020 20:31:45

%S 1,361,1819441,43710250585,3210080802962401,563561785768079119561,

%T 202205968733586788098486801,132994909755454702268136738753721,

%U 148026526435655214537290625514621562305,262237873172349351865682580536682974917045801,704454843460345510903820429747302209179158476142321

%N a(n) = (4*n+2)! * Sum_{k=0..n} 1 / (4*k+2)!.

%F E.g.f.: (1/2) * (cosh(x) - cos(x)) / (1 - x^4) = x^2/2! + 361*x^6/6! + 1819441*x^10/10! + 43710250585*x^14/14! + ...

%F a(n) = floor(c * (4*n+2)!), where c = (cosh(1) - cos(1)) / 2 = A334364.

%t Table[(4 n + 2)! Sum[1/(4 k + 2)!, {k, 0, n}], {n, 0, 10}]

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

%t Table[Floor[(1/2) (Cosh[1] - Cos[1]) (4 n + 2)!], {n, 0, 10}]

%o (PARI) a(n) = (4*n+2)!*sum(k=0, n, 1/(4*k+2)!); \\ _Michel Marcus_, Sep 17 2020

%Y Cf. A000522, A051396, A051397, A087350, A330045, A334364, A337725, A337726, A337727, A337728, A337730.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Sep 17 2020