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A119309
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a(n) = binomial(2*n,n) * 6^n.
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3
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1, 12, 216, 4320, 90720, 1959552, 43110144, 960740352, 21616657920, 489977579520, 11171488813056, 255928652808192, 5886359014588416, 135839054182809600, 3143703825373593600, 72933928748667371520
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OFFSET
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0,2
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COMMENTS
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Number of lattice paths from (0,0) to (n,n) using three kinds of steps (1,0) and two kinds of steps (0,1). - Joerg Arndt, Jul 01 2011
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LINKS
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FORMULA
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D-finite with recurrence: n*a(n) +12*(-2*n+1)*a(n-1)=0. - R. J. Mathar, Jan 20 2020
Sum_{n>=0} 1/a(n) = 24/23 + 24*sqrt(23)*arcsin(1/sqrt(24))/529.
Sum_{n>=0} (-1)^n/a(n) = 24/25 - 24*arcsinh(1/sqrt(24))/125. (End)
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EXAMPLE
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a(3) = binomial(2*3,3) * (6^3) = 20 * 216 = 4320. - Indranil Ghosh, Mar 03 2017
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MATHEMATICA
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Table[Binomial[2n, n]*(6^n), {n, 0, 15}] (* Indranil Ghosh, Mar 03 2017 *)
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PROG
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(PARI) /* same as in A092566 but use */
steps=[[1, 0], [1, 0], [1, 0], [0, 1], [0, 1]]; /* note repeated entries */
(Python)
import math
f=math.factorial
def C(n, r): return f(n)//f(r)//f(n-r)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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