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%I #9 Sep 24 2013 10:13:45
%S 1,2,1,3,1,2,1,2,3,4,3,5,2,2,1,5,1,6,3,4,5,4,1,6,4,2,5,9,7,2,1,9,8,8,
%T 10,17,10,8,7,11,5,10,7,7,10,4,3,12,8,7,12,8,1,10,12,18,18,11,10,14,
%U 10,2,1,16,19,22,14,12,15,17,9,22,14,10,19,15,9,16,9,2,27,23,18,26,25,20,14,22
%N Number of positive integer coefficients in n-th Bernoulli polynomial.
%C This is, more explicitly, the number of positive integers of the form C(n+1,i)*B(i) where B(i) is the i-th Bernoulli number and C(n,k) is the binomial coefficient (k -sets from n distinct elements). The floor((n-1)/2) zero cases are excluded from this sequence. - _Olivier Gérard_, Oct 19 2005
%D R. L. Graham et al., Concrete Math., Chapter 6.5, Bernoulli numbers
%e B(5,x)=x^5 - (5/2)*x^4 +( 5/3)*x^3 +0*x^2- (1/6)*x+0 hence a(5)=1
%t Table[Count[ DeleteCases[ Table[Binomial[j + 1, i]*BernoulliB[ i], {i, 0, j}], 0], _Integer], {j, 0, 200}] (Gerard)
%o (PARI) B(n,x)=sum(i=0,n,binomial(n,i)*bernfrac(i)*x^(n-i)); a(n)=sum(i=0,n,if(frac(polcoeff(B(n,x),i)),0,1))-floor((n-1)/2)
%Y Cf. A027641, A027642.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Jun 19 2004
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