|
| |
|
|
A111160
|
|
G.f.: C - Z; where C is the g.f. for the Catalan numbers (A000108) and Z is the g.f. for A055113 with offset 0.
|
|
3
| |
|
|
0, 1, 1, 4, 9, 31, 91, 309, 1009, 3481, 11956, 42065, 148655, 532039, 1915369, 6950452, 25357233, 93034813, 342888250, 1269246437, 4715945712, 17583623988, 65766726906, 246694006971, 927801717255, 3497918129001, 13217196871126, 50046561077947
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
COMMENTS
| Expressible in terms of ballot numbers.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
Douglas Rogers, Comments on A111160, A055113 and A006013
|
|
|
FORMULA
| Let C := (1 - sqrt(1 - 4*x)) / (2*x), Z := (- 1/4 - (1/4)*(1 - 4*x)^(1/2) + (1/4)*(2 + 2*(1 - 4*x)^(1/2) + 12*x)^(1/2))/x; g.f. is W := C - Z.
G.f.: -((-3 + sqrt(1 - 4x) + sqrt(2)*sqrt(1 + sqrt(1 - 4x) + 6x))/(4x)).
|
|
|
MATHEMATICA
| CoefficientList[ Series[ -((-3 + Sqrt[1 - 4*x] + Sqrt[2]*Sqrt[1 + Sqrt[1 - 4x] + 6x])/(4x)), {x, 0, 10}], x] (* Robert G. Wilson v *)
|
|
|
CROSSREFS
| Cf. A055113, A006013.
Sequence in context: A042599 A145543 A141043 * A192876 A201689 A071378
Adjacent sequences: A111157 A111158 A111159 * A111161 A111162 A111163
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), following a suggestion from Douglas Rogers, Oct 22 2005
|
| |
|
|
