OFFSET
0,2
COMMENTS
B(n,p)=sum(i=0,n,p^i*sum(j=0,i,binomial(n,j)*B(j))) where B(k)=k-th Bernoulli number. B(2n,p)/B(2n) take integer values for all n if p=1,2,3,4,6. p=5 is the smallest integer for which B(2n,5)/B(2n) is not always integer valued.
FORMULA
a(n) = [(1/16)*(21-sqrt(5))*25^n+(1/8)*sqrt(5)*((25/4)^n+(25/9)^n-(25/16)^n)-(1/16)*(5-sqrt(5))+(1/4)*sqrt(5)*(25/36)^n)]
PROG
(PARI) a(n)=floor(sum(i=0, 2*n, 5^i*sum(j=0, i, binomial(2*n, j)*bernfrac(j)))/bernfrac(2*n))
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jun 17 2004
STATUS
approved