A092399 Row 5 of array in A288580.

1, 1, 2, -6, -4, -25, -24, -42, 336, 216, 2500, 2376, 4032, -52416, -33264, -562500, -532224, -891072, 16039296, 10112256, 225000000, 212357376, 352864512, -8115883776, -5096577024, -140625000000, -132511002624, -219128861952, 6135608134656, 3842819076096, 126562500000000

Offset: 0

Author

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

Keywords

• sign

Examples

			!11!_5 = 11(11-5)(11-10)(11-15)(11-20) = 11(6)(1)(-4)(-9) = 2376.
		

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(5); # N. J. A. Sloane, Jul 03 2017

Formula

a(n) = !n!5 = Prod{i=0, 1, 2, ... .}_{0<|n-5i|<=n}(n-5i) = n(n-5)(n-10)....

Extensions

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