

A094959


Number of positive integer coefficients in nth Bernoulli polynomial.


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 ith Bernoulli number and C(n,k) is the binomial coefficient (k sets from n distinct elements). The floor((n1)/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^(ni)); a(n)=sum(i=0, n, if(frac(polcoeff(B(n, x), i)), 0, 1))floor((n1)/2)


CROSSREFS

Cf. A027641, A027642.
Sequence in context: A184169 A176207 A059130 * A162696 A108103 A111376
Adjacent sequences: A094956 A094957 A094958 * A094960 A094961 A094962


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Jun 19 2004


STATUS

approved



