A113265 Partial sums of Catalan numbers A000108 multiplied by powers of -6.

1, -5, 67, -1013, 17131, -309461, 5849131, -114243413, 2287607467, -46710150485, 968879741611, -20358507992405, 432438339283627, -9270351245202773, 200309903779703467, -4358060643012007253, 95389812498547780267, -2099063396615767545173

Offset: 0

Author

Wolfdieter Lang, Oct 31 2005

Keywords

• sign
• easy

Comments

Seventh column (m=6) of triangle A112707 (partial sums of Catalan numbers multiplied by powers of nonpositive numbers).

Crossrefs

Cf. A113264 (m=5).

Formula

a(n)= A112707(n+6, 6), n>=0.

G.f.: c(-6*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(6*x)/(1+x), hence |a(n)| is the convolution of the sequences {C(n)*6^n} and {(-1)^n}, where C(n):=A000108(n).