|
Search: id:A096049
|
|
|
| A096049 |
|
a(n)= [B(2n,5)/B(2n)] ( [x]=floor(x), see comment for B(n,k) definition ). |
|
+0
4
|
|
| 1, 31, 745, 18397, 458545, 11455304, 286331664, 7157976493, 178947452208, 4473674081283, 111841775707840, 2796043915880138, 69901094917491465, 1747527354316971026, 43688183741551848165, 1092204592811481165247
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
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)]
|
|
PROGRAM
|
(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
|
Cf. A096045, A096046, A096047, A096048.
Sequence in context: A000565 A014930 A061252 this_sequence A166488 A051587 A069380
Adjacent sequences: A096046 A096047 A096048 this_sequence A096050 A096051 A096052
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 17 2004
|
|
|
Search completed in 0.002 seconds
|
