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%I #26 May 24 2022 12:54:53
%S 1,7,47,5923,426457,15636757,7318002277,1536780478171,603180793741,
%T 142957467201379447,60042136224579367741,10127106976545720025649,
%U 18228792557782296046168201,12796612375563171824410077103,3463616416319098507140327535879,1380498543075754976417359117871773
%N a(n) is the numerator of Sum_{k=0..n} 1 / (2*k+1)!.
%F Numerators of coefficients in expansion of sinh(sqrt(x)) / (sqrt(x) * (1 - x)).
%e 1, 7/6, 47/40, 5923/5040, 426457/362880, 15636757/13305600, 7318002277/6227020800, ...
%t Table[Sum[1/(2 k + 1)!, {k, 0, n}], {n, 0, 15}] // Numerator
%t nmax = 15; CoefficientList[Series[Sinh[Sqrt[x]]/(Sqrt[x] (1 - x)), {x, 0, nmax}], x] // Numerator
%o (PARI) a(n) = numerator(sum(k=0, n, 1/(2*k+1)!)); \\ _Michel Marcus_, May 24 2022
%o (Python)
%o from fractions import Fraction
%o from math import factorial
%o def A354211(n): return sum(Fraction(1,factorial(2*k+1)) for k in range(n+1)).numerator # _Chai Wah Wu_, May 24 2022
%Y Cf. A009445, A053557, A061354, A073742, A103816, A120265, A143382, A289381, A354331 (denominators), A354332, A354334.
%K nonn,frac
%O 0,2
%A _Ilya Gutkovskiy_, May 24 2022
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