cp's OEIS Frontend

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.

A096046 a(n) = B(2n,3)/B(2n) (see comment).

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%I A096046 #18 Sep 08 2022 08:45:14
%S A096046 1,15,141,1275,11481,103335,930021,8370195,75331761,677985855,
%T A096046 6101872701,54916854315,494251688841,4448265199575,40034386796181,
%U A096046 360309481165635,3242785330490721,29185067974416495,262665611769748461
%N A096046 a(n) = B(2n,3)/B(2n) (see comment).
%C A096046 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.
%H A096046 Vincenzo Librandi, <a href="/A096046/b096046.txt">Table of n, a(n) for n = 0..1000</a>
%F A096046 a(n) = (1/4)*(7*9^n - 3).
%F A096046 a(n) = 10*a(n-1) - 9*a(n-2); a(0)=1, a(1)=15.
%F A096046 a(n) = 9*a(n-1) + 6. First differences = 14*A001019(n). - _Paul Curtz_, Jul 07 2008
%o A096046 (PARI) a(n)=sum(i=0,2*n,3^i*sum(j=0,i,binomial(2*n,j)*bernfrac(j)))/bernfrac(2*n)
%o A096046 (Magma) [(1/4)*(7*9^n-3): n in [0..30]]; // _Vincenzo Librandi_, Aug 13 2011
%o A096046 (Maxima) A096046(n):=(1/4)*(7*9^n-3)$ makelist(A096046(n),n,0,30); /* _Martin Ettl_, Nov 13 2012 */
%Y A096046 Cf. A096045, A096047, A096048.
%K A096046 nonn
%O A096046 0,2
%A A096046 _Benoit Cloitre_, Jun 17 2004