%I #18 Sep 08 2022 08:45:14

%S 1,15,141,1275,11481,103335,930021,8370195,75331761,677985855,

%T 6101872701,54916854315,494251688841,4448265199575,40034386796181,

%U 360309481165635,3242785330490721,29185067974416495,262665611769748461

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

%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.

%H Vincenzo Librandi, <a href="/A096046/b096046.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = (1/4)*(7*9^n - 3).

%F a(n) = 10*a(n-1) - 9*a(n-2); a(0)=1, a(1)=15.

%F a(n) = 9*a(n-1) + 6. First differences = 14*A001019(n). - _Paul Curtz_, Jul 07 2008

%o (PARI) a(n)=sum(i=0,2*n,3^i*sum(j=0,i,binomial(2*n,j)*bernfrac(j)))/bernfrac(2*n)

%o (Magma) [(1/4)*(7*9^n-3): n in [0..30]]; // _Vincenzo Librandi_, Aug 13 2011

%o (Maxima) A096046(n):=(1/4)*(7*9^n-3)$ makelist(A096046(n),n,0,30); /* _Martin Ettl_, Nov 13 2012 */

%Y Cf. A096045, A096047, A096048.

%K nonn

%O 0,2

%A _Benoit Cloitre_, Jun 17 2004