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, k) = !n!_k = Prod_{i=0, 1, 2, .., floor(2n/k)}_{0<|n-i*k|<=n} (n-i*k) = n(n-k)(n-2k)(n-3k)... . k=8.
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(8); # N. J. A. Sloane, Jul 03 2017
PROG
(PARI) a(n, k)=prod(j=0, (2*n)\k, if(n-k*j==0, 1, n-k*j))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, M.L. Perez and Amarnath Murthy, Mar 27 2004
EXTENSIONS
Entry revised by N. J. A. Sloane, Jul 03 2017
STATUS
approved