A113265 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A113265

Partial sums of Catalan numbers A000108 multiplied by powers of -6.

1, -5, 67, -1013, 17131, -309461, 5849131, -114243413, 2287607467, -46710150485, 968879741611, -20358507992405, 432438339283627, -9270351245202773, 200309903779703467, -4358060643012007253, 95389812498547780267, -2099063396615767545173

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Seventh column (m=6) of triangle A112707 (partial sums of Catalan numbers multiplied by powers of nonpositive numbers).

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n)= A112707(n+6, 6), n>=0.

G.f.: c(-6*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(6*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*6^n} and {(-1)^n}, where C(n):=A000108(n).

CROSSREFS