A113266 Partial sums of Catalan numbers A000108 multiplied by powers of -7.

1, -6, 92, -1623, 31991, -673903, 14855765, -338444182, 7905221248, -188294015986, 4556160266218, -111682969647780, 2767470863606632, -69211374967753668, 1744655539982525892, -44282217426880817943, 1130756774785983371727

Offset

0,2

Comments

Eighth column (m=7) of triangle A112707 (partial sums of Catalan numbers multiplied by powers of nonpositive numbers).

Links

Table of n, a(n) for n=0..16.

Formula

a(n)= A112707(n+7, 7), n>=0.

G.f.: c(-7*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(7*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*7^n} and {(-1)^n}, where C(n):=A000108(n).

Crossrefs

Cf. A113265 (m=6).

Sequence in context: A171910 A278683 A280214 * A009607 A009684 A221080

Adjacent sequences: A113263 A113264 A113265 * A113267 A113268 A113269

Keyword

sign,easy

Author

Wolfdieter Lang, Oct 31 2005

Status

approved