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

1, 15, 141, 1275, 11481, 103335, 930021, 8370195, 75331761, 677985855, 6101872701, 54916854315, 494251688841, 4448265199575, 40034386796181, 360309481165635, 3242785330490721, 29185067974416495, 262665611769748461

Offset: 0

Author

Benoit Cloitre, Jun 17 2004

Keywords

• nonn

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.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A096045, A096047, A096048.

Programs

Magma

[(1/4)*(7*9^n-3): n in [0..30]]; // Vincenzo Librandi, Aug 13 2011

Maxima

A096046(n):=(1/4)*(7*9^n-3)$ makelist(A096046(n),n,0,30); /* Martin Ettl, Nov 13 2012 */

PARI

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

Formula

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

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

a(n) = 9*a(n-1) + 6. First differences = 14*A001019(n). - Paul Curtz, Jul 07 2008