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A096049
a(n)= [B(2n,5)/B(2n)] ( [x]=floor(x), see comment for B(n,k) definition ).
3
1, 31, 745, 18397, 458545, 11455304, 286331664, 7157976493, 178947452208, 4473674081283, 111841775707840, 2796043915880138, 69901094917491465, 1747527354316971026, 43688183741551848165, 1092204592811481165247
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