|
|
A050511
|
|
a(n) = (-1)^n * Sum_{i=0..n} binomial(n+1,i+1)*Catalan(i).
|
|
2
|
|
|
1, -3, 8, -23, 74, -262, 993, -3943, 16178, -68000, 291191, -1265618, 5568263, -24749363, 110961248, -501209303, 2278704938, -10419244888, 47882934663, -221047167628, 1024586641973, -4766517165713, 22248226873538, -104160733650738, 489007907489239
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
REFERENCES
|
J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 371.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (sqrt((5*x+1)/(x+1))-1)/(2*x*(x+1)).
(n+1)*a(n)=(1-6*n)*a(n-1)-5*n*a(n-2)+(-1)^n. - Vladeta Jovovic, Jul 16 2004
a(n) ~ (-1)^n * 5^(n+5/2) / (32 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Mar 02 2014
|
|
MATHEMATICA
|
Table[(-1)^n Sum[Binomial[n+1, i+1]CatalanNumber[i], {i, 0, n}], {n, 0, 30}] (* Harvey P. Dale, Jan 26 2013 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|