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 A059837 #17 Jul 02 2025 16:02:01
%S A059837 1,1,4,18,144,1200,14400,176400,2822400,45722880,914457600,
%T A059837 18441561600,442597478400,10685567692800,299195895398400,
%U A059837 8414884558080000,269276305858560000,8646761377013760000,311283409572495360000
%N A059837 Diagonal T(s,s) of triangle A059836.
%D A059837 S. G. Mikhlin, Constants in Some Inequalities of Analysis, Wiley, NY, 1986, see p. 59.
%F A059837 T(s, s) = (s-1)^2 * T(s-1, s-1) / floor(s/2) - Larry Reeves.
%F A059837 a(n) = Sum_{k=0..n} (-1)^(n+k)*C(n, k)*Sum_{i=0..n} C(n, floor(i/2))*k^i. - _Paul Barry_, Aug 05 2004
%F A059837 a(n) = (n-1)!*binomial(n-1,floor(n-1,2)), n>=1.
%F A059837 E.g.f. is the integral of the o.g.f. of A001405. With offset 0: e.g.f. is o.g.f. of A001405.
%F A059837 Conjecture: +(n+1)*a(n) -2*n*a(n-1) -4*n*(n-1)^2*a(n-2)=0. - _R. J. Mathar_, Nov 24 2012
%p A059837 T := proc(s,t) option remember: if s=1 or t=1 then RETURN(1) fi: if t>1 and t mod 2 = 1 then RETURN(product((s-i)^2, i=1..(t-1)/2)) else RETURN((s-t/2)*product((s-i)^2, i=1..t/2-1)) fi: end: for s from 1 to 50 do printf(`%d,`, T(s,s)) od:
%t A059837 a[n_] := (n-1)! Binomial[n-1, Quotient[n-1, 2]];
%t A059837 Table[a[n], {n, 1, 19}] (* _Jean-François Alcover_, Apr 29 2023 *)
%Y A059837 Cf. A059836.
%K A059837 nonn,easy
%O A059837 1,3
%A A059837 _N. J. A. Sloane_, Feb 25 2001
%E A059837 More terms from _James Sellers_, Feb 26 2001 and from Larry Reeves (larryr(AT)acm.org), Feb 26 2001