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

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

Offset: 0

Author

Wolfdieter Lang, Oct 31 2005

Keywords

• sign
• easy

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).