|
|
A112710
|
|
Partial sums of Catalan numbers A000108 multiplied by powers of -3.
|
|
2
|
|
|
1, -2, 16, -119, 1015, -9191, 87037, -851186, 8531044, -87167702, 904619302, -9509144240, 101036961052, -1083385595648, 11708378016712, -127402051267703, 1394629704432367, -15347719608268403, 169699299111055897, -1884322608673443833, 21003350078068124587
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Fourth column (m=3) of triangle A112707 (partial sums of Catalan numbers multiplied by powers of nonpositive numbers).
|
|
LINKS
|
|
|
FORMULA
|
G.f.: c(-3*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(3*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*3^n} and {(-1)^n}, where C(n):=A000108(n).
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|