A112699 Partial sum of Catalan numbers A000108 multiplied by powers of 5.

1, 6, 56, 681, 9431, 140681, 2203181, 35718806, 594312556, 10090406306, 174113843806, 3044524000056, 53828703687556, 960689055250056, 17284175383375056, 313147365080640681, 5708299647795484431

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

a(n) = Sum_{k=0,..,n} C(k)*5^k, n>=0, with C(n):=A000108(n).

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.

Recurrence: (n+1)*a(n) = 3*(7*n-3)*a(n-1) - 10*(2*n-1)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ 20^(n+1)/(19*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012

Mathematica

CoefficientList[Series[(1-Sqrt[1-20*x])/(10*x)/(1-x), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)

Prog

(PARI) x='x+O('x^50); Vec((1-sqrt(1-20*x))/(10*x*(1-x))) \\ G. C. Greubel, Mar 17 2017

Crossrefs

Sixth column (m=5) of triangle A112705.

Sequence in context: A053336 A290788 A215507 * A093197 A303921 A052317

Adjacent sequences: A112696 A112697 A112698 * A112700 A112701 A112702

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 31 2005

Status

approved