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A096049 a(n)= [B(2n,5)/B(2n)] ( [x]=floor(x), see comment for B(n,k) definition ). 3

%I

%S 1,31,745,18397,458545,11455304,286331664,7157976493,178947452208,

%T 4473674081283,111841775707840,2796043915880138,69901094917491465,

%U 1747527354316971026,43688183741551848165,1092204592811481165247

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

%C 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.

%F 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)]

%o (PARI) a(n)=floor(sum(i=0,2*n,5^i*sum(j=0,i,binomial(2*n,j)*bernfrac(j)))/bernfrac(2*n))

%Y Cf. A096045, A096046, A096047, A096048.

%K nonn

%O 0,2

%A _Benoit Cloitre_, Jun 17 2004

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Last modified October 30 18:13 EDT 2020. Contains 338090 sequences. (Running on oeis4.)