OFFSET
0,3
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.
FORMULA
a(n) = !n!_4 = Prod_{i=0, 1, 2, ... .}_{0<|n-4i|<=n}(n-4i) = n*(n-4)*(n-8)....
EXAMPLE
!9!_4 = 9*(9-4)*(9-8)*(9-12)*(9-16) = 9*(5)*(1)*(-3)*(-7) = 945.
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;
r:=k->[seq(T(n, k), n=0..60)]; r(4); # N. J. A. Sloane, Jul 03 2017
MATHEMATICA
T[n_, k_] := Module[{i, p = 1},
For[i = 0, i <= Floor[2 n/k], i++,
If[n - k i != 0, p *= (n - k i)]]; p];
T[_, 0] = 1;
a[n_] := T[n, 4];
Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Feb 16 2023 *)
CROSSREFS
KEYWORD
sign
AUTHOR
J. Dezert (Jean.Dezert(AT)onera.fr), Mar 21 2004
EXTENSIONS
Entry revised by N. J. A. Sloane, Jul 03 2017
STATUS
approved