cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

1, -6, 92, -1623, 31991, -673903, 14855765, -338444182, 7905221248, -188294015986, 4556160266218, -111682969647780, 2767470863606632, -69211374967753668, 1744655539982525892, -44282217426880817943, 1130756774785983371727
Offset: 0

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Author

Wolfdieter Lang, Oct 31 2005

Keywords

Comments

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

Crossrefs

Cf. A113265 (m=6).

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).
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