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A059836
Triangle T(s,t), s >= 1, 1 <= t <= s (see formula line).
1
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
1,5
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
Cf. A059837.
Sequence in context: A360859 A209573 A100075 * A069270 A079901 A121426
KEYWORD
nonn,easy,tabl
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