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A112698 Partial sum of Catalan numbers A000108 multiplied by powers of 4. 1
1, 5, 37, 357, 3941, 46949, 587621, 7616357, 101332837, 1375876965, 18987759461, 265554114405, 3755416368997, 53610591434597, 771525112379237, 11181285666076517, 163041321978836837, 2390321854565988197 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) = Sum_{k=0,..,n} C(k)*4^k, n>=0, with C(n):=A000108(n).

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.

Recurrence: (n+1)*a(n) = (17*n-7)*a(n-1) - 8*(2*n-1)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ 16^(n+1)/(15*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012

MATHEMATICA

CoefficientList[Series[(1-Sqrt[1-16*x])/(8*x)/(1-x), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)

PROG

(PARI) x='x+O('x^50); Vec((1-sqrt(1-16*x))/(8*x*(1-x))) \\ G. C. Greubel, Mar 17 2017

CROSSREFS

Fifth column (m=4) of triangle A112705.

Sequence in context: A004208 A198077 A208813 * A234953 A025168 A084358

Adjacent sequences:  A112695 A112696 A112697 * A112699 A112700 A112701

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 31 2005

STATUS

approved

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Last modified February 21 00:32 EST 2018. Contains 299388 sequences. (Running on oeis4.)