|
Search: id:A127927
|
|
|
| A127927 |
|
G.f. A(x) satisfies: [x^(2n)] A(x)/Catalan(x)^n = A001764(n) = C(3n,n)/(2n+1) and [x^(2n+1)] A(x)/Catalan(x)^n = A001764(n+1) for n>=0, where Catalan(x) is the g.f. of A000108. |
|
+0
2
|
|
| 1, 1, 3, 9, 31, 108, 391, 1431, 5319, 19926, 75252, 285750, 1090491, 4177774, 16060401, 61916977, 239307063, 926929746, 3597296770, 13984508500, 54448030092, 212282062488, 828673761978, 3238495227846, 12669206034339
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Main diagonal of triangle A062745: a(n) = A062745(n,n) (see formula given in A062745 by Emeric Deutsch).
|
|
FORMULA
|
a(n) = C(2n,n) - (-1)^(n-1)*Sum_{i=0..[(n-1)/2]} C(3i,i)*C(i-n-1,n-1-2i)/(2i+1).
|
|
PROGRAM
|
(PARI) {a(n)=binomial(2*n, n)+(-1)^n*sum(i=0, (n-1)\2, binomial(3*i, i)*binomial(i-n-1, n-1-2*i)/(2*i+1))}
|
|
CROSSREFS
|
Cf. A062745; A001764 (ternary trees), A000108 (Catalan).
Adjacent sequences: A127924 A127925 A127926 this_sequence A127928 A127929 A127930
Sequence in context: A027033 A027096 A130620 this_sequence A123222 A112566 A128082
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Feb 06 2007
|
|
|
Search completed in 0.002 seconds
|
