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!_3 = Prod_{i=0, 1, 2, ... .}_{0<|n-3i|<=n}(n-3i) = n(n-3)(n-6)...
EXAMPLE
!7!_3 = 7(7-3)(7-6)(7-9)(7-12) = 7(4)(1)(-2)(-5) = 280.
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(3); # N. J. A. Sloane, Jul 03 2017
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