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A112697 Partial sum of Catalan numbers (A000108) multiplied by powers of 3. 1
1, 4, 22, 157, 1291, 11497, 107725, 1045948, 10428178, 106126924, 1097913928, 11511677470, 122057782762, 1306480339462, 14098243951822, 153208673236237, 1675240428936307, 18417589741637077, 203464608460961377 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} C(k)*3^k, n>=0, with C(n) = A000108(n).
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).
Recurrence: (n+1)*a(n) = (13*n-5)*a(n-1) - 6*(2*n-1)*a(n-2). - Vaclav Kotesovec, Oct 19 2012
a(n) ~ 12^(n+1)/(11*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012
MATHEMATICA
CoefficientList[Series[(1-Sqrt[1-12*x])/(6*x)/(1-x), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)
PROG
(PARI) x='x+O('x^50); Vec((1-sqrt(1-12*x))/(6*x*(1-x))) \\ G. C. Greubel, Mar 17 2017
CROSSREFS
Fourth column (m=3) of triangle A112705.
Cf. A000108.
Sequence in context: A052650 A198053 A197925 * A327994 A113717 A124563
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 31 2005
STATUS
approved

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Last modified May 25 17:00 EDT 2024. Contains 372804 sequences. (Running on oeis4.)