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A186266
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Expansion of 2F1( 1/2, 3/2; 4; 16*x ).
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1
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1, 3, 18, 140, 1260, 12474, 132132, 1472328, 17065620, 204155380, 2506399896, 31443925968, 401783498480, 5215458874500, 68633685693000, 914099013896400, 12304253831789700, 167193096184907100, 2291164651422801000, 31637804708163654000, 439903041116118980400
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OFFSET
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0,2
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COMMENTS
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Combinatorial interpretation welcome.
Could involve planar maps, lattice walks, interpretations of catalan numbers.
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LINKS
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FORMULA
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D-finite with recurrence n*(n+3)*a(n) -4*(2*n-1)*(2*n+1)*a(n-1)=0. - R. J. Mathar, Jun 17 2016
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MATHEMATICA
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CoefficientList[
Series[HypergeometricPFQ[{1/2, 3/2}, {4}, 16*x], {x, 0, 20}], x]
Table[3 CatalanNumber[n] CatalanNumber[n+1] * (n+1) / (n+3), {n, 0, 20}] (* Indranil Ghosh, Mar 05 2017 *)
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PROG
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(PARI)
c(n) = binomial(2*n, n) / (n+1);
a(n) = 3 * c(n) * c(n+1) *(n+1) / (n+3); \\ Indranil Ghosh, Mar 05 2017
(Python)
import math
f=math.factorial
def C(n, r): return f(n) / f(r) / f(n-r)
def Catalan(n): return C(2*n, n) / (n+1)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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