A092397 Row 3 of array in A288580.

1, 1, -2, -9, -8, 40, 324, 280, -2240, -26244, -22400, 246400, 3779136, 3203200, -44844800, -850305600, -717516800, 12197785600, 275499014400, 231757926400, -4635158528000, -121495065350400, -101973487616000, 2345390215168000, 69981157641830400, 58634755379200000

Offset: 0

Author

J. Dezert (Jean.Dezert(AT)onera.fr), Mar 21 2004

Keywords

• sign

Examples

			!7!_3 = 7(7-3)(7-6)(7-9)(7-12) = 7(4)(1)(-2)(-5) = 280.
		

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.

Crossrefs

Cf. A288580.

Programs

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

Formula

a(n) = !n!3 = Prod{i=0, 1, 2, ... .}_{0<|n-3i|<=n}(n-3i) = n(n-3)(n-6)...

Extensions

Entry revised by N. J. A. Sloane, Jul 03 2017