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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 (list; graph; refs; listen; history; text; internal format)
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..15.

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

Cf. A096045, A096046, A096047, A096048.

Sequence in context: A014930 A196988 A061252 * A166488 A051587 A069380

Adjacent sequences:  A096046 A096047 A096048 * A096050 A096051 A096052

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jun 17 2004

STATUS

approved

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Last modified September 25 10:38 EDT 2020. Contains 337337 sequences. (Running on oeis4.)