|
Search: id:A094959
|
|
|
| A094959 |
|
Number of positive integer coefficients in n-th Bernoulli polynomial. |
|
+0
3
|
|
| 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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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 (ogerard(AT)ext.jussieu.fr), Oct 19 2005
|
|
REFERENCES
|
R. L. Graham et al., Concrete Math., Chapter 6.5, Bernoulli numbers
|
|
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)
|
|
PROGRAM
|
(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: A089242 A029423 A059130 this_sequence A108103 A111376 A001511
Adjacent sequences: A094956 A094957 A094958 this_sequence A094960 A094961 A094962
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 19 2004
|
|
|
Search completed in 0.002 seconds
|
