A094959 Number of positive integer coefficients in n-th Bernoulli polynomial.

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, 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, 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

Offset: 1

Author

Benoit Cloitre, Jun 19 2004

Keywords

• nonn

Comments

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

Examples

			B(5,x)=x^5 - (5/2)*x^4 +( 5/3)*x^3 +0*x^2- (1/6)*x+0 hence a(5)=1
		

References

• R. L. Graham et al., Concrete Math., Chapter 6.5, Bernoulli numbers

Crossrefs

Cf. A027641, A027642.

Programs

Mathematica

Table[Count[ DeleteCases[ Table[Binomial[j + 1, i]*BernoulliB[ i], {i, 0, j}], 0], _Integer], {j, 0, 200}] (Gerard)

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)