|
|
A360083
|
|
a(n) = Sum_{k=0..n} binomial(5*k,n-k) * Catalan(k).
|
|
3
|
|
|
1, 1, 7, 35, 189, 1092, 6538, 40278, 253730, 1626858, 10582616, 69669273, 463319257, 3107941405, 21004392887, 142882885210, 977562617826, 6722361860888, 46438235933700, 322111000796428, 2242538435656450, 15665017062799230, 109761527468995102
(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)^5 * A(x)).
G.f.: 2 / (1 + sqrt( 1 - 4*x*(1+x)^5 )).
|
|
PROG
|
(PARI) a(n) = sum(k=0, n, binomial(5*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)^5)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|