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%I #14 Dec 07 2019 12:18:27
%S 0,1,3,9,105,315,4095,11025,348705,1545075,17931375,93087225,
%T 3764185425,45589819275,1060569885375,15877899662625,900941666625,
%U 5722531807867875,90088576482279375,1688777976676415625,18148954872023600625,320586579951629866875,11054393914490520969375
%N a(n) = (2*n-1)!! mod n!, where double factorial is A006882.
%C (2n-1)!! is the product of first n odd numbers.
%e a(4) = 1*3*5*7 mod (1*2*3*4) = 105 mod 24 = 9.
%t o = 1; Reap[For[n = 1, n <= 99, n += 2, o *= n; m = Mod[o, (Quotient[n, 2] + 1)!]; Sow[m]]][[2, 1]] (* _Jean-François Alcover_, Oct 05 2017, translated from _Alex Ratushnyak_'s Python code *)
%o (Python)
%o import math
%o o=1
%o for n in range(1,99,2):
%o o*=n
%o print str(o % math.factorial(n//2+1))+',',
%Y Cf. A006882, A232618, A024502 (floor((2*n-1)!! / n!)).
%K nonn
%O 1,3
%A _Alex Ratushnyak_, Nov 28 2013
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