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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A113268 Partial sums of Catalan numbers A000108 multiplied by powers of -9.

Original entry on oeis.org

1, -8, 154, -3491, 88363, -2391695, 67758517, -1984135184, 59572675846, -1824065741672, 56739965057524, -1788027005117150, 56960705737368622, -1831391418128245478, 59351217395117651362, -1936731395137029733043, 63581744945624043237427
Offset: 0

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Author

Wolfdieter Lang, Oct 31 2005

Keywords

Comments

Tenth column (m=9) of triangle A112707 (partial sums of Catalan numbers multiplied by powers of nonpositive numbers).

Crossrefs

Cf. A113267 (m=8).

Formula

a(n)= A112707(n+9, 9), n>=0.
G.f.: c(-9*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(9*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*9^n} and {(-1)^n}, where C(n):=A000108(n).
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