A096049 a(n) = [B(2n,5)/B(2n)] ( [x] = floor(x), see comment for B(n,k) definition ).

1, 31, 745, 18397, 458545, 11455304, 286331664, 7157976493, 178947452208, 4473674081283, 111841775707840, 2796043915880138, 69901094917491465, 1747527354316971026, 43688183741551848165, 1092204592811481165247, 27305114815741345242261, 682627870365123204281633

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.

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = floor((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

Cf. A096045, A096046, A096047, A096048.

Sequence in context: A196988 A358179 A061252 * A166488 A051587 A069380

Adjacent sequences: A096046 A096047 A096048 * A096050 A096051 A096052

Keyword

nonn

Author

Benoit Cloitre, Jun 17 2004

Status

approved