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a(n) = numerator(r(n)) where r(n) = Sum_{j=0..n} j!/(2^j*floor(j/2)!)^2.
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%I #14 Oct 03 2019 06:51:50

%S 1,5,11,47,191,779,1563,6287,50331,201639,403341,1614057,6456459,

%T 25828839,51658107,206638863,3306228243,13225022367,26450056889,

%U 105800458501,423201880193,1692808490741,3385617069661,13542470306761,108339763130127,433359069421483

%N a(n) = numerator(r(n)) where r(n) = Sum_{j=0..n} j!/(2^j*floor(j/2)!)^2.

%F Lim_{n -> oo} r(n) = (4/3)^(3/2) = A118273.

%e r(n) = 1, 5/4, 11/8, 47/32, 191/128, 779/512, 1563/1024, 6287/4096, 50331/32768, 201639/131072, ...

%p A327494 := n -> numer(add(j!/(2^j*iquo(j,2)!)^2, j=0..n)):

%p seq(A327494(n), n=0..25);

%o (PARI) a(n)={ numerator(sum(j=0, n, j!/(2^j*(j\2)!)^2)) } \\ _Andrew Howroyd_, Sep 28 2019

%o (Julia)

%o A327494(n) = sum(<<(A163590(k), A327492(n) - A327492(k)) for k in 0:n) # _Peter Luschny_, Oct 03 2019

%Y Denominators are in A327493.

%Y Cf. A327491, A327492, A327493, A327495, A118273, A163590.

%K nonn,frac

%O 0,2

%A _Peter Luschny_, Sep 27 2019