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a(n) is the denominator of Sum_{k=0..n} (-1)^k / (2*k)!.
1

%I #7 May 25 2022 09:08:14

%S 1,2,24,720,8064,3628800,479001600,87178291200,20922789888000,

%T 1280474741145600,2432902008176640000,1124000727777607680000,

%U 620448401733239439360000,403291461126605635584000000,60977668922342772100300800000,1569543549184562477137920000000

%N a(n) is the denominator of Sum_{k=0..n} (-1)^k / (2*k)!.

%F Denominators of coefficients in expansion of cos(sqrt(x)) / (1 - x).

%e 1, 1/2, 13/24, 389/720, 4357/8064, 1960649/3628800, 258805669/479001600, ...

%t Table[Sum[(-1)^k/(2 k)!, {k, 0, n}], {n, 0, 15}] // Denominator

%t nmax = 15; CoefficientList[Series[Cos[Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Denominator

%o (PARI) a(n) = denominator(sum(k=0, n, (-1)^k/(2*k)!)); \\ _Michel Marcus_, May 24 2022

%Y Cf. A010050, A049470, A053556, A061355, A143383, A354138 (numerators), A354331, A354333, A354335.

%K nonn,frac

%O 0,2

%A _Ilya Gutkovskiy_, May 24 2022