|
|
A185994
|
|
A generalized q-Catalan number for q=2.
|
|
1
|
|
|
1, 2, 6, 26, 150, 1114, 10614, 131002, 2128278, 46294426, 1368718518, 55647242106, 3137452915158, 246751601425242, 27181289502625014, 4205716133932054842, 915890632125187606038, 281117681559174501597466, 121733516122198763782243638
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 1/(1-2x/(1-x/(1-4x/(1-2x/(1-8x/(1-4x/(1-16x/(1-8x/(1-... (continued fraction).
G.f.: 1/(1-2x-2x^2/(1-5x-8x^2/(1-10x-32x^2/(1-(2^2+2^4)x-2^7x^2/(1-(2^3+2^5)x-2^9x^2/(1-.... (continued fraction).
a(n)=if(n=0,1,2*a(n-1)+sum{k=0..n-2, 2^k*a(k)*a(n-1-k)}).
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|