A113269 Partial sums of Catalan numbers A000108 multiplied by powers of -10.

1, -9, 191, -4809, 135191, -4064809, 127935191, -4162064809, 138837935191, -4723162064809, 163236837935191, -5715363162064809, 202296636837935191, -7226703363162064809, 260217296636837935191, -9434627703363162064809, 344142072296636837935191

Offset: 0

Author

Wolfdieter Lang, Oct 31 2005

Keywords

• sign
• easy

Comments

Eleventh column (m=10) of triangle A112707 (partial sums of Catalan numbers multiplied by powers of nonpositive numbers).

Crossrefs

Cf. A113268 (m=9).

Formula

a(n)= A112707(n+10, 10), n>=0.

G.f.: c(-10*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(10*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*10^n} and {(-1)^n}, where C(n):=A000108(n).