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, 2363990505927736155, 21275914553349625401

Offset

0,2

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

Index entries for linear recurrences with constant coefficients, signature (10,-9).

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

From Elmo R. Oliveira, Dec 10 2025: (Start)

G.f.: (5*x+1)/((9*x-1)*(x-1)).

E.g.f.: exp(x)*(7*exp(8*x) - 3)/4.

a(n) = A199565(n) - 1 = (A198964(n) - 1)/2 = (A199566(n) - 2)/2. (End)

Mathematica

A096046[n_] := (7*9^n - 3)/4; Array[A096046, 25, 0] (* or *)
NestList[9*# + 6 &, 1, 24] (* Paolo Xausa, Feb 09 2026 *)

Prog

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

Crossrefs

Cf. A096045, A096047, A096048.

Cf. A001019, A198964, A199565, A199566.

Sequence in context: A055903 A320818 A026859 * A093117 A045724 A241402

Adjacent sequences: A096043 A096044 A096045 * A096047 A096048 A096049

Keyword

nonn,easy

Author

Benoit Cloitre, Jun 17 2004

Status

approved