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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
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