|
|
A000777
|
|
a(n) = (n+2)*Catalan(n) - 1.
|
|
3
|
|
|
1, 2, 7, 24, 83, 293, 1055, 3860, 14299, 53481, 201551, 764217, 2912167, 11143499, 42791039, 164812364, 636438059, 2463251009, 9552773999, 37112526989, 144410649239, 562724141459, 2195581527359, 8576490341249, 33537507830423, 131272552839203, 514285886020255
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
Boothby, T.; Burkert, J.; Eichwald, M.; Ernst, D. C.; Green, R. M.; Macauley, M. On the cyclically fully commutative elements of Coxeter groups, J. Algebr. Comb. 36, No. 1, 123-148 (2012), Table 1 type B.
|
|
FORMULA
|
D-finite with recurrence: (n+1)*a(n) + 4*(-3*n+1)*a(n-1) + 5*(9*n-13)*a(n-2) + 2*(-29*n+72)*a(n-3) + 12*(2*n-7)*a(n-4) = 0. - R. J. Mathar, Jun 11 2019
|
|
MAPLE
|
[seq((binomial(2*n, n)/(n+1))*(n+2)-1, n=0..27)]; # Zerinvary Lajos, Jun 25 2006
|
|
MATHEMATICA
|
Table[(n + 2)*CatalanNumber[n] - 1, {n, 0, 20}] (* T. D. Noe, Jun 20 2012 *)
|
|
PROG
|
(PARI) a(n) = (n+2)*binomial(2*n, n)/(n+1) - 1; \\ Michel Marcus, Sep 11 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|