A113267 Partial sums of Catalan numbers A000108 multiplied by powers of -8.

1, -7, 121, -2439, 54905, -1321351, 33281657, -866396551, 23125022329, -629441571207, 17405126104697, -487562768820615, 13806913025988217, -394606681111406983, 11367704830045574777, -329739328993506896263, 9622560010799553435257

Offset: 0

Author

Wolfdieter Lang, Oct 31 2005

Keywords

• sign
• easy

Comments

Ninth column (m=8) of triangle A112707 (partial sums of Catalan numbers multiplied by powers of nonpositive numbers).

Crossrefs

Cf. A113266 (m=7).

Formula

a(n)= A112707(n+8, 8), n>=0.

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).