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A059836 Triangle T(s,t), s >= 1, 1 <= t <= s (see formula line).

%I A059836 #15 Jul 02 2025 16:02:01
%S A059836 1,1,1,1,2,4,1,3,9,18,1,4,16,48,144,1,5,25,100,400,1200,1,6,36,180,
%T A059836 900,3600,14400,1,7,49,294,1764,8820,44100,176400,1,8,64,448,3136,
%U A059836 18816,112896,564480,2822400,1,9,81,648,5184,36288,254016,1524096,9144576
%N A059836 Triangle T(s,t), s >= 1, 1 <= t <= s (see formula line).
%D A059836 S. G. Mikhlin, Constants in Some Inequalities of Analysis, Wiley, NY, 1986, see p. 59.
%F A059836 T(s, t) = (s-1)^2*(s-2)^2*...*(s-(t-1)/2)^2 if t odd, else (s-1)^2*(s-2)^2*...*(s-t/2+1)^2*(s-t/2).
%e A059836 Triangle begins:
%e A059836   1;
%e A059836   1,1;
%e A059836   1,2,4;
%e A059836   1,3,9,18;
%e A059836   ...
%p A059836 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 15 do for t from 1 to s do printf(`%d,`, T(s,t)) od:od:
%t A059836 T[s_, t_] := If[OddQ[t], Times @@ (s - Range[(t - 1)/2])^2, Times @@ (s - Range[t/2 - 1])^2*(s - t/2)];
%t A059836 Table[T[s, t], {s, 1, 15}, {t, 1, s}] // Flatten (* _Jean-François Alcover_, Apr 29 2023 *)
%Y A059836 Cf. A059837.
%K A059836 nonn,easy,tabl
%O A059836 1,5
%A A059836 _N. J. A. Sloane_, Feb 25 2001
%E A059836 More terms from _James Sellers_, Feb 26 2001 and from Larry Reeves (larryr(AT)acm.org), Feb 26 2001