Search: id:A094959
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%I A094959
%S A094959 1,2,1,3,1,2,1,2,3,4,3,5,2,2,1,5,1,6,3,4,5,4,1,6,4,2,5,9,7,2,1,9,8,8,10,
%T A094959 17,10,8,7,11,5,10,7,7,10,4,3,12,8,7,12,8,1,10,12,18,18,11,10,14,10,2,
               1,
%U A094959 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 A094959 Number of positive integer coefficients in n-th Bernoulli polynomial.
%C A094959 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 
               GERARD (olivier.gerard(AT)gmail.com), Oct 19 2005
%D A094959 R. L. Graham et al., Concrete Math., Chapter 6.5, Bernoulli numbers
%e A094959 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 A094959 Table[Count[ DeleteCases[ Table[Binomial[j + 1, i]*BernoulliB[ i], {i, 
               0, j}], 0], _Integer], {j, 0, 200}] (Gerard)
%o A094959 (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 A094959 Cf. A027641, A027642.
%Y A094959 Sequence in context: A089242 A029423 A059130 this_sequence A162696 A108103 
               A111376
%Y A094959 Adjacent sequences: A094956 A094957 A094958 this_sequence A094960 A094961 
               A094962
%K A094959 nonn
%O A094959 1,2
%A A094959 Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 19 2004

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