This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A353921 #8 May 16 2022 04:32:05 %S A353921 0,1,2,3,20,202,2953,58574,1517830,49788988,2016610506,98842394546, %T A353921 5766037456673,394787840828770,31350291022336674,2858009622374873775, %U A353921 296454369597967332107,34715387135986234970960,4557676382296459474148951,666708107998151285537770827 %N 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). %C A353921 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. %F A353921 A005439(n-1) <= a(n) <= A005439(n). %F A353921 A110501(n) <= a(n) <= A110501(n+1). %F A353921 a(n) ~ ((2*n)/(exp(1)*Pi))^(2*n)*(11/6 + 8*n - 23/(576*n)). %p A353921 z := n -> (2^(2*n + 1/2) - 1)*(4*n + 1)*Zeta(1/2 - 2*n): %p A353921 a := n -> ifelse(n < 4, n, floor(abs(z(n)))): %p A353921 seq(floor(evalf(a(n))), n = 0..19); %Y A353921 Cf. A005439, A110501. %K A353921 nonn %O A353921 0,3 %A A353921 _Peter Luschny_, May 14 2022