A092398 Row 4 of array in A288580.

1, 1, -4, -3, -16, -15, 144, 105, 1024, 945, -14400, -10395, -147456, -135135, 2822400, 2027025, 37748736, 34459425, -914457600, -654729075, -15099494400, -13749310575, 442597478400, 316234143225, 8697308774400, 7905853580625, -299195895398400, -213458046676875, -6818690079129600, -6190283353629375

Offset: 0

Author

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

Keywords

• sign

Examples

			!9!_4 = 9*(9-4)*(9-8)*(9-12)*(9-16) = 9*(5)*(1)*(-3)*(-7) = 945.
		

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(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 *)

Formula

a(n) = !n!4 = Prod{i=0, 1, 2, ... .}_{0<|n-4i|<=n}(n-4i) = n*(n-4)*(n-8)....

Extensions

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