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a(n) is the denominator of Sum_{k=0..n} 1 / (2*k)!.
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%I #12 May 24 2022 12:55:14

%S 1,2,24,720,4480,518400,479001600,29059430400,20922789888000,

%T 6402373705728000,810967336058880000,1124000727777607680000,

%U 88635485961891348480000,14936720782466875392000000,27717122237428532772864000000,265252859812191058636308480000000

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

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

%e 1, 3/2, 37/24, 1111/720, 6913/4480, 799933/518400, 739138093/479001600, ...

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

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

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

%o (Python)

%o from fractions import Fraction

%o from math import factorial

%o def A354335(n): return sum(Fraction(1,factorial(2*k)) for k in range(n+1)).denominator # _Chai Wah Wu_, May 24 2022

%Y Cf. A010050, A053556, A061355, A073743, A143383, A354331, A354333, A354334 (numerators).

%K nonn,frac

%O 0,2

%A _Ilya Gutkovskiy_, May 24 2022