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) = (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
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
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jun 17 2004
STATUS
approved