OFFSET
1,5
REFERENCES
S. G. Mikhlin, Constants in Some Inequalities of Analysis, Wiley, NY, 1986, see p. 59.
FORMULA
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).
EXAMPLE
Triangle begins:
1;
1,1;
1,2,4;
1,3,9,18;
...
MAPLE
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:
MATHEMATICA
T[s_, t_] := If[OddQ[t], Times @@ (s - Range[(t - 1)/2])^2, Times @@ (s - Range[t/2 - 1])^2*(s - t/2)];
Table[T[s, t], {s, 1, 15}, {t, 1, s}] // Flatten (* Jean-François Alcover, Apr 29 2023 *)
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Feb 25 2001
EXTENSIONS
More terms from James A. Sellers, Feb 26 2001 and from Larry Reeves (larryr(AT)acm.org), Feb 26 2001
STATUS
approved