A353921 a(n) = n if n < 4, otherwise floor(abs(z(n))) where z(n) = (2^(2*n + 1/2) - 1)*(4*n + 1)*zeta(1/2 - 2*n).

0, 1, 2, 3, 20, 202, 2953, 58574, 1517830, 49788988, 2016610506, 98842394546, 5766037456673, 394787840828770, 31350291022336674, 2858009622374873775, 296454369597967332107, 34715387135986234970960, 4557676382296459474148951, 666708107998151285537770827

Offset: 0

Author

Peter Luschny, May 14 2022

Keywords

• nonn

Comments

a(n) gives an integer valued definition of what may be called a 'Genocchi half integer', i.e. it tries to give the expression 'G(n + 1/2)' a meaning, where G(n) = A110501(n) are the Genocchi numbers. Consider also the sequence of Genocchi median numbers A005439.

Crossrefs

Cf. A005439, A110501.

Programs

Maple

z := n -> (2^(2*n + 1/2) - 1)*(4*n + 1)*Zeta(1/2 - 2*n):
a := n -> ifelse(n < 4, n, floor(abs(z(n)))):
seq(floor(evalf(a(n))), n = 0..19);

Formula

A005439(n-1) <= a(n) <= A005439(n).

A110501(n) <= a(n) <= A110501(n+1).

a(n) ~ ((2*n)/(exp(1)*Pi))^(2*n)*(11/6 + 8*n - 23/(576*n)).