A092971 Row 6 of array in A288580.

1, 1, 2, -9, -8, -5, -36, -35, -64, 729, 640, 385, 5184, 5005, 8960, -164025, -143360, -85085, -1679616, -1616615, -2867200, 72335025, 63078400, 37182145, 967458816, 929553625, 1640038400, -52732233225, -45921075200, -26957055125, -870712934400, -835668708875, -1469474406400, 57425401982025

Offset: 0

Author

Paul D. Hanna 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, A092972, A092973, 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(6); # 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=6.

Extensions

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