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A092397 Row 3 of array in A288580. 9
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 (list; graph; refs; listen; history; text; internal format)
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: A300780 A272347 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

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Last modified February 3 15:47 EST 2023. Contains 360035 sequences. (Running on oeis4.)