|
| |
|
|
A050478
|
|
a(n) = C(n)*(8n+1) where C(n)=Catalan numbers (A000108).
|
|
2
|
|
|
|
1, 9, 34, 125, 462, 1722, 6468, 24453, 92950, 354926, 1360476, 5231954, 20177164, 78004500, 302211720, 1173076245, 4561139430, 17761336230, 69257611500, 270391268070, 1056823387620
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
|
|
|
LINKS
|
|
|
|
FORMULA
|
-(n+1)*(8*n-7)*a(n) + 2*(8*n+1)*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Dec 03 2014
G.f.: (7 - 12*x - 7*sqrt(1 - 4*x))/(2*x*sqrt(1 - 4*x)). - Ilya Gutkovskiy, Jun 13 2017
|
|
|
MATHEMATICA
|
Table[CatalanNumber[n](8n+1), {n, 0, 20}] (* Harvey P. Dale, May 20 2012 *)
|
|
|
PROG
|
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); (Coefficients(R!( (7-12*x-7*Sqrt(1-4*x))/(2*x*Sqrt(1-4*x)))))// Marius A. Burtea, Jan 05 2020
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
