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

1,2

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

References

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

Links

Table of n, a(n) for n=1..88.

Example

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

Mathematica

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

Prog

(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)

Crossrefs

Cf. A027641, A027642.

Sequence in context: A184169 A176207 A059130 * A162696 A370265 A364447

Adjacent sequences: A094956 A094957 A094958 * A094960 A094961 A094962

Keyword

nonn

Author

Benoit Cloitre, Jun 19 2004

Status

approved