A337728 - OEIS

%I #8 Sep 17 2020 20:31:36

%S 1,121,365905,6278929801,358652470233121,51516840824285500441,

%T 15640512874253077933887601,8915467710633236496186345872425,

%U 8755702529258688898174686554391144001,13878488965077362598718732163634314533105081,33731389859841228248933904149069928786421237268881

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

%F 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! + ...

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

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

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

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

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

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

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Sep 17 2020