A059836 - OEIS

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

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OFFSET

1,5

REFERENCES

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

LINKS

Table of n, a(n) for n=1..54.

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;

1,2,4;

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

Adjacent sequences: A059833 A059834 A059835 * A059837 A059838 A059839

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