OFFSET
0,6
REFERENCES
F. Smarandache, Back and Forth Factorials, Arizona State Univ., Special Collections, 1972.
LINKS
J. Dezert, ed., Smarandacheials (1), Mathematics Magazine for Grades 1-12, No. 4, 2004.
J. Dezert, ed., Smarandacheials (2), Mathematics Magazine for Grades 1-12, No. 4, 2004.
EXAMPLE
Array begins:
1, -1, 4, -36, 576, -14400, 518400, -25401600, 1625702400, -131681894400, ...
1, -1, -4, 9, 64, -225, -2304, 11025, 147456, -893025, -14745600, 108056025, ...
1, 1, -2, -9, -8, 40, 324, 280, -2240, -26244, -22400, 246400, 3779136, ...
1, 1, -4, -3, -16, -15, 144, 105, 1024, 945, -14400, -10395, -147456, ...
1, 1, 2, -6, -4, -25, -24, -42, 336, 216, 2500, 2376, 4032, ...
1, 1, 2, -9, -8, -5, -36, -35, -64, 729, 640, 385, 5184, ...
1, 1, 2, 3, -12, -10, -6, -49, -48, -90, -120, 1320, 1080, ...
1, 1, 2, 3, -16, -15, -12, -7, -64, -63, -120, -165, 2304, ...
1, 1, 2, 3, 4, -20, -18, -14, -8, -81, -80, -154, -216, ...
1, 1, 2, 3, 4, -25, -24, -21, -16, -9, -100, -99, -192, ...
...
MAPLE
T:=proc(n, k) local i, p;
p:=1;
for i from 0 to floor(2*n/k) do
if n-k*i <> 0 then p:=p*(n-k*i) fi; od:
p;
end;
scan1:=proc(a, M1) local lis, n, k; lis:=[]; for n from 1 to M1 do for k from 0 to n-1 do
lis:=[op(lis), a(k, n-k)]; od: od: lis; end:
scan1(T, 12);
MATHEMATICA
T[n_, k_] := Module[{i, p = 1}, For[i = 0, i <= Floor[2n/k], i++, If[n - k i != 0, p *= (n - k i)]]; p]; T[_, 0] = 1;
Table[T[k, n - k + 1], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 05 2020, after Maple *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
N. J. A. Sloane, Jul 03 2017
STATUS
approved