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

0,3

References

F. Smarandache, Back and Forth Factorials, Arizona State Univ., Special Collections, 1972.

Links

Table of n, a(n) for n=0..25.

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.

Formula

a(n) = !n!_3 = Prod_{i=0, 1, 2, ... .}_{0<|n-3i|<=n}(n-3i) = n(n-3)(n-6)...

Example

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

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

Crossrefs

Cf. A288580.

Sequence in context: A272347 A371255 A214300 * A272348 A351166 A092270

Adjacent sequences: A092394 A092395 A092396 * A092398 A092399 A092400

Keyword

sign

Author

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

Extensions

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

Status

approved