A113264 Partial sums of Catalan numbers A000108 multiplied by powers of -5.

1, -4, 46, -579, 8171, -123079, 1939421, -31576204, 527017546, -8969076204, 155054361296, -2715355794954, 48068823892546, -858791527669954, 15464694800455046, -280398494896810579, 5114753787818033171, -93796371395287435579, 1728250671451392251921

Offset: 0

Author

Wolfdieter Lang, Oct 31 2005

Keywords

• sign
• easy

Comments

Sixth column (m=5) of triangle A112707 (partial sums of Catalan numbers multiplied by powers of nonpositive numbers).

Crossrefs

Cf. A112711 (m=4).

Formula

a(n)= A112707(n+5, 5), n>=0.

G.f.: c(-5*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(5*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*5^n} and {(-1)^n}, where C(n):=A000108(n).