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%I #9 Jul 03 2017 16:12:29
%S 1,1,-2,-9,-8,40,324,280,-2240,-26244,-22400,246400,3779136,3203200,
%T -44844800,-850305600,-717516800,12197785600,275499014400,
%U 231757926400,-4635158528000,-121495065350400,-101973487616000,2345390215168000,69981157641830400,58634755379200000
%N Row 3 of array in A288580.
%D F. Smarandache, Back and Forth Factorials, Arizona State Univ., Special Collections, 1972.
%H J. Dezert, ed., <a href="http://www.mathematicsmagazine.com/corresp/J_Dezert/JDezert.htm">Smarandacheials (1)</a>, Mathematics Magazine for Grades 1-12, No. 4, 2004.
%H J. Dezert, ed., <a href="http://www.mathematicsmagazine.com/corresp/J_Dezert/JDezert2.htm">Smarandacheials (2)</a>, Mathematics Magazine for Grades 1-12, No. 4, 2004.
%F a(n) = !n!_3 = Prod_{i=0, 1, 2, ... .}_{0<|n-3i|<=n}(n-3i) = n(n-3)(n-6)...
%e !7!_3 = 7(7-3)(7-6)(7-9)(7-12) = 7(4)(1)(-2)(-5) = 280.
%p T:=proc(n,k) local i,p;
%p p:=1;
%p for i from 0 to floor(2*n/k) do
%p if n-k*i <> 0 then p:=p*(n-k*i) fi; od:
%p p;
%p end;
%p r:=k->[seq(T(n,k), n=0..60)]; r(3); # _N. J. A. Sloane_, Jul 03 2017
%Y Cf. A288580.
%K sign
%O 0,3
%A J. Dezert (Jean.Dezert(AT)onera.fr), Mar 21 2004
%E Entry revised by _N. J. A. Sloane_, Jul 03 2017
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