login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A137571 Main diagonal of square array A137570. 3
1, 2, 10, 60, 397, 2802, 20710, 158428, 1244413, 9980220, 81394123, 672998498, 5628741195, 47535483498, 404790717079, 3471892750622, 29966295451511, 260080708564964, 2268416956569463, 19872441881999354, 174783803353387498 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A variant is A007857, the number of independent sets in rooted plane trees on n nodes.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

G.f. A(x) = 1/(1 - x*C(x)*F(x)^2 - x*F(x)^3), where C(x) = 1 + xC(x)^2 is g.f. of Catalan numbers (A000108) and F(x) = 1 + xF(x)^4 is g.f. of A002293.

EXAMPLE

G.f.: A(x) = 1 + 2*x + 10*x^2 + 60*x^3 + 397*x^4 + 2802*x^5 +...;

A(x) = 1/(1 - x*C(x)*F(x)^2 - x*F(x)^3), where

C(x) = 1 + xC(x)^2 is g.f. of Catalan numbers (A000108):

[1, 1, 2, 5, 14, 42, 132, 429, 1430, ..., C(2n,n)/(n+1), ...] and

F(x) = 1 + xF(x)^4 is g.f. of A002293:

[1, 1, 4, 22, 140, 969, 7084, 53820, ..., C(4n,n)/(3n+1), ...].

PROG

(PARI) {a(n)=local(m=n+1, C, F, A); C=Ser(vector(m, r, binomial(2*r-2, r-1)/r)); F=Ser(vector(m, r, binomial(4*r-4, r-1)/(3*r-2))); A=1/(1-x*C*F^2-x*F^3); polcoeff(A+O(x^m), n, x)}

CROSSREFS

Cf. A137570, A137572, A137573; A007857 (variant); A000108, A002293.

Sequence in context: A173613 A004981 A214764 * A215002 A301625 A262001

Adjacent sequences:  A137568 A137569 A137570 * A137572 A137573 A137574

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 27 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 31 08:46 EDT 2020. Contains 338101 sequences. (Running on oeis4.)