|
|
A113267
|
|
Partial sums of Catalan numbers A000108 multiplied by powers of -8.
|
|
1
|
|
|
1, -7, 121, -2439, 54905, -1321351, 33281657, -866396551, 23125022329, -629441571207, 17405126104697, -487562768820615, 13806913025988217, -394606681111406983, 11367704830045574777, -329739328993506896263, 9622560010799553435257
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Ninth column (m=8) of triangle A112707 (partial sums of Catalan numbers multiplied by powers of nonpositive numbers).
|
|
LINKS
|
|
|
FORMULA
|
G.f.: c(-8*x)/(1-x), where c(x):=(1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers A000108.
G.f. for unsigned sequence: c(8*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*8^n} and {(-1)^n}, where C(n):=A000108(n).
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|