A092973 Row 8 of array in A288580.

1, 1, 2, 3, -16, -15, -12, -7, -64, -63, -120, -165, 2304, 2145, 1680, 945, 16384, 16065, 30240, 40755, -921600, -855855, -665280, -369495, -9437184, -9237375, -17297280, -23108085, 722534400, 670134465, 518918400, 286358625, 9663676416, 9449834625, 17643225600, 23454706275, -936404582400

Offset: 0

Author

Paul D. Hanna, M.L. Perez and Amarnath Murthy, Mar 27 2004

Keywords

• sign

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, A092396, A092397, A092398, A092399, A092971, A092972, A092974.

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

PARI

a(n,k)=prod(j=0,(2*n)\k,if(n-k*j==0,1,n-k*j))

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.

Extensions

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