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

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, 900, 3600, 14400, 1, 7, 49, 294, 1764, 8820, 44100, 176400, 1, 8, 64, 448, 3136, 18816, 112896, 564480, 2822400, 1, 9, 81, 648, 5184, 36288, 254016, 1524096, 9144576

Offset: 1

Author

N. J. A. Sloane, Feb 25 2001

Keywords

• nonn
• easy
• tabl

Examples

			Triangle begins:
  1;
  1,1;
  1,2,4;
  1,3,9,18;
  ...
		

References

• S. G. Mikhlin, Constants in Some Inequalities of Analysis, Wiley, NY, 1986, see p. 59.

Crossrefs

Cf. A059837.

Programs

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 *)

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).

Extensions

More terms from James Sellers, Feb 26 2001 and from Larry Reeves (larryr(AT)acm.org), Feb 26 2001