|
Search: id:A162162
|
|
|
| A162162 |
|
G.f. satisfies: A(x) = Catalan(x + x^2 + x^3*A(x)) where Catalan(x) = (1-sqrt(1-4*x))/(2x) is the g.f. of A000108. |
|
+0
2
|
|
| 1, 1, 3, 10, 36, 139, 560, 2328, 9914, 43027, 189619, 846267, 3817105, 17373048, 79687447, 367991891, 1709477714, 7983062151, 37454903501, 176470241003, 834601583199, 3960757007408, 18855383609076, 90019104197240
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} Sum_{j=0..k} C(2*n-2*k+j+1,n-k)/(2*n-2*k+j+m) * C(n-k,k-j)*C(k-j,j).
Let A(x)^m = Sum_{n>=0} a(n,m)*x^n/n!, then
a(n,m) = Sum_{k=0..n} Sum_{j=0..k} C(2*n-2*k+j+m,n-k)*m/(2*n-2*k+j+m) * C(n-k,k-j)*C(k-j,j).
|
|
EXAMPLE
|
G.f.: A(x) = 1 + x + 3*x^2 + 10*x^3 + 36*x^4 + 139*x^5 + 560*x^6 +...
A(x) = Catalan(x + x^2 + x^3*A(x)) where:
Catalan(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +...
|
|
PROGRAM
|
(PARI) {a(n, m=1)=sum(k=0, n, sum(j=0, k, binomial(2*n-2*k+j+m, n-k)*m/(2*n-2*k+j+m)*binomial(n-k, k-j)*binomial(k-j, j)))}
|
|
CROSSREFS
|
Cf. A000108.
Sequence in context: A002212 A149041 A129247 this_sequence A149042 A081921 A165792
Adjacent sequences: A162159 A162160 A162161 this_sequence A162163 A162164 A162165
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jun 26 2009
|
|
|
Search completed in 0.002 seconds
|
