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!)
A153392 G.f.: A(x) = F(x*G(x)^3) where F(x) = G(x*F(x)) = 1 + x*F(x)^3 is the g.f. of A001764 and G(x) = F(x/G(x)) = 1 + x*G(x)^2 is the g.f. of A000108 (Catalan). 2
1, 1, 6, 39, 272, 2001, 15333, 121266, 983274, 8133564, 68382628, 582700485, 5021538753, 43690059657, 383263396836, 3386175566418, 30104702903914, 269125162789764, 2417709649413102, 21815252320257250, 197620659225838530 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) = Sum_{k=0..n} C(3k+1,k)/(3k+1) * C(2n+k,n-k)*3k/(2n+k) for n>0 with a(0)=1.

G.f. satisfies: A(x) = 1 + x*G(x)^3*A(x)^3 where G(x) is the g.f. of A000108.

G.f. satisfies: A(x*F(x)) = F(x*F(x)^4) where F(x) is the g.f. of A001764.

EXAMPLE

G.f.: A(x) = F(x*G(x)^3) = 1 + x + 6*x^2 + 39*x^3 + 272*x^4+... where

F(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 +...

F(x)^3 = 1 + 3*x + 12*x^2 + 55*x^3 + 273*x^4 + 1428*x^5 +...

G(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +...

G(x)^2 = 1 + 2*x + 5*x^2 + 14*x^3 + 42*x^4 + 132*x^5 + 429*x^6 +...

G(x)^3 = 1 + 3*x + 9*x^2 + 28*x^3 + 90*x^4 + 297*x^5 + 1001*x^6 +...

A(x)^2 = 1 + 2*x + 13*x^2 + 90*x^3 + 658*x^4 + 5014*x^5 +...

A(x)^3 = 1 + 3*x + 21*x^2 + 154*x^3 + 1176*x^4 + 9264*x^5 +...

G(x)^3*A(x)^3 = 1 + 6*x + 39*x^2 + 272*x^3 + 2001*x^4 + 15333*x^5 +...

PROG

(PARI) {a(n)=if(n==0, 1, sum(k=0, n, binomial(3*k+1, k)/(3*k+1)*binomial(2*(n-k)+3*k, n-k)*3*k/(2*(n-k)+3*k)))}

CROSSREFS

Cf. A000108, A001764; A153391, A153393.

Sequence in context: A264232 A068765 A006633 * A253077 A231482 A122827

Adjacent sequences:  A153389 A153390 A153391 * A153393 A153394 A153395

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 15 2009

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 September 27 13:39 EDT 2020. Contains 337380 sequences. (Running on oeis4.)