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%I #12 May 13 2013 01:49:55
%S 1,0,1,1,3,2,4,6,8,8,10,4,6,12,8,4,24,4,8,24,32,16,24,96,32,48,24,16,
%T 384,32,64,144,16,8,36,128,16,80,24,16,96,32,16,96,4,16,448,128,64,24,
%U 192,48,192,64,16,96,768,32,96,32,64
%N Number of odd divisors of !n.
%C !k is a subfactorial number (A000166).
%e a(7) = 6 because the divisors of !7 = 1854 are {1, 2, 3, 6, 9, 18, 103, 206, 309, 618, 927, 1854} with 6 odd divisors 1, 3, 9, 103, 309 and 927 => 6 is in the sequence.
%t f[n_] := Block[{d = Divisors[Subfactorial[n]]}, Count[OddQ[d], True]]; Table[f[n], {n, 0, 60}]
%o (PARI) a(n)=if(n<2,1-n,my(x='x,k=n!*polcoeff(exp(-x+x*O(x^n))/(1-x),n));numdiv(k>>valuation(k,2))) \\ _Charles R Greathouse IV_, Sep 13 2011
%Y Cf. A000166, A195207.
%K nonn
%O 0,5
%A _Michel Lagneau_, Sep 13 2011
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