This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A096049 #10 Jan 14 2025 20:45:17
%S A096049 1,31,745,18397,458545,11455304,286331664,7157976493,178947452208,
%T A096049 4473674081283,111841775707840,2796043915880138,69901094917491465,
%U A096049 1747527354316971026,43688183741551848165,1092204592811481165247,27305114815741345242261,682627870365123204281633
%N A096049 a(n) = [B(2n,5)/B(2n)] ( [x] = floor(x), see comment for B(n,k) definition ).
%C A096049 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 A096049 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).
%o A096049 (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 A096049 Cf. A096045, A096046, A096047, A096048.
%K A096049 nonn
%O A096049 0,2
%A A096049 _Benoit Cloitre_, Jun 17 2004