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A096045 a(n) = B(2*n,2)/B(2*n) (see comment). 17
1, 10, 46, 190, 766, 3070, 12286, 49150, 196606, 786430, 3145726, 12582910, 50331646, 201326590, 805306366, 3221225470, 12884901886, 51539607550, 206158430206, 824633720830, 3298534883326, 13194139533310, 52776558133246 (list; graph; refs; listen; history; text; internal format)
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

FORMULA

a(n) = 3*4^n - 2; a(0)=1 a(1)=10.

a(n) = 5*a(n-1) - 4*a(n-2).

a(n) = 4a(n-1) + 6. First differences give A002063. - Paul Curtz, Jul 07 2008

MATHEMATICA

a[n_] := Sum[2^k*Sum[Binomial[2*n, j]*BernoulliB[j], {j, 0, k}], {k, 0, 2*n}]/BernoulliB[2*n]; Table[a[n], {n, 0, 22}] (* Jean-Fran├žois Alcover, Jan 14 2015 *)

NestList[4#+6&, 1, 30] (* Harvey P. Dale, Dec 27 2016 *)

PROG

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

(MAGMA) [3*4^n-2: n in [0..30]]; // Vincenzo Librandi, Aug 13 2011

(Maxima) A096045(n):=3*4^n-2$ makelist(A096045(n), n, 0, 30); /* Martin Ettl, Nov 13 2012 */

CROSSREFS

Cf. A096046, A096047, A096048.

Sequence in context: A103501 A219003 A003197 * A287090 A183133 A115712

Adjacent sequences:  A096042 A096043 A096044 * A096046 A096047 A096048

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, Jun 17 2004

STATUS

approved

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Last modified June 23 21:09 EDT 2021. Contains 345402 sequences. (Running on oeis4.)