A112710 Partial sums of Catalan numbers A000108 multiplied by powers of -3.

1, -2, 16, -119, 1015, -9191, 87037, -851186, 8531044, -87167702, 904619302, -9509144240, 101036961052, -1083385595648, 11708378016712, -127402051267703, 1394629704432367, -15347719608268403, 169699299111055897, -1884322608673443833, 21003350078068124587

Offset: 0

Author

Wolfdieter Lang, Oct 31 2005

Keywords

• sign
• easy

Comments

Fourth column (m=3) of triangle A112707 (partial sums of Catalan numbers multiplied by powers of nonpositive numbers).

Crossrefs

Cf. A064306 (unsigned m=2 case).

Formula

a(n)= A112707(n+3, 3), n>=0.

G.f.: c(-3*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(3*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*3^n} and {(-1)^n}, where C(n):=A000108(n).