%I A059837
%S A059837 1,1,4,18,144,1200,14400,176400,2822400,45722880,914457600,18441561600,
%T A059837 442597478400,10685567692800,299195895398400,8414884558080000,
%U A059837 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 (pbarry(AT)wit.ie), 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.
%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:
%Y A059837 Cf. A059836.
%Y A059837 Sequence in context: A156445 A143992 A060841 this_sequence A054759 A007153 
               A156870
%Y A059837 Adjacent sequences: A059834 A059835 A059836 this_sequence A059838 A059839 
               A059840
%K A059837 nonn,easy
%O A059837 1,3
%A A059837 N. J. A. Sloane (njas(AT)research.att.com), Feb 25 2001
%E A059837 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 26 2001 
               and from Larry Reeves (larryr(AT)acm.org), Feb 26 2001.