A092974 - OEIS

%I #8 Jul 03 2017 16:12:05

%S 1,1,2,3,4,-20,-18,-14,-8,-81,-80,-154,-216,-260,3640,3240,2464,1360,

%T 26244,25840,49280,68040,80080,-1841840,-1632960,-1232000,-671840,

%U -19131876,-18811520,-35728000,-48988800,-57097040,1827105280,1616630400,1214752000,658403200,24794911296,24360918400

%N Row 9 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, 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=9.

%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(9); # _N. J. A. Sloane_, Jul 03 2017

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

%Y Cf. A288580, A092396, A092397, A092398, A092399, A092971, A092972, A092973.

%K sign

%O 0,3

%A Paul D. Hanna, M.L. Perez and _Amarnath Murthy_, Mar 27 2004