A327494 a(n) = numerator(r(n)) where r(n) = Sum_{j=0..n} j!/(2^j*floor(j/2)!)^2.

1, 5, 11, 47, 191, 779, 1563, 6287, 50331, 201639, 403341, 1614057, 6456459, 25828839, 51658107, 206638863, 3306228243, 13225022367, 26450056889, 105800458501, 423201880193, 1692808490741, 3385617069661, 13542470306761, 108339763130127, 433359069421483

Offset: 0

Author

Peter Luschny, Sep 27 2019

Keywords

• nonn
• frac

Examples

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

Crossrefs

Denominators are in A327493.

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

Programs

Julia

A327494(n) = sum(<<(A163590(k), A327492(n) - A327492(k)) for k in 0:n) # Peter Luschny, Oct 03 2019

Maple

A327494 := n -> numer(add(j!/(2^j*iquo(j,2)!)^2, j=0..n)):
seq(A327494(n), n=0..25);

PARI

a(n)={ numerator(sum(j=0, n, j!/(2^j*(j\2)!)^2)) } \\ Andrew Howroyd, Sep 28 2019

Formula

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