A112711 Partial sums of Catalan numbers A000108 multiplied by powers of -4.

1, -3, 29, -291, 3293, -39715, 500957, -6527779, 87188701, -1187355427, 16424527069, -230141827875, 3259720426717, -46595454638883, 671319066305757, -9738441487391523, 142121594825368797, -2085158937761782563, 30737922595101500637, -455043684091275090723

Offset: 0

Author

Wolfdieter Lang, Oct 31 2005

Keywords

• sign
• easy

Comments

Fifth column (m=4) of triangle A112707 (partial sums of Catalan numbers multiplied by powers of nonpositive numbers).

Crossrefs

Cf. A112710 (m=3).

Formula

a(n)= A112707(n+4, 4), n>=0.

G.f.: c(-4*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(4*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*4^n} and {(-1)^n}, where C(n):=A000108(n).