|
| |
|
|
A360076
|
|
a(n) = Sum_{k=0..n} binomial(3*k,n-k) * Catalan(k).
|
|
4
|
|
|
|
1, 1, 5, 20, 90, 430, 2136, 10937, 57307, 305822, 1656482, 9083432, 50328114, 281324294, 1584578746, 8984740485, 51242962251, 293772468164, 1691974930584, 9785378133297, 56805049768157, 330880419984832, 1933299689139364, 11328101469158554
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
|
|
|
FORMULA
|
G.f. A(x) satisfies A(x) = 1/(1 - x * (1+x)^3 * A(x)).
G.f.: 2 / (1 + sqrt( 1 - 4*x*(1+x)^3 )).
|
|
|
PROG
|
(PARI) a(n) = sum(k=0, n, binomial(3*k, n-k)*binomial(2*k, k)/(k+1));
(PARI) my(N=30, x='x+O('x^N)); Vec(2/(1+sqrt(1-4*x*(1+x)^3)))
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
