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A220910
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Matchings avoiding the pattern 231.
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3
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1, 1, 3, 14, 83, 570, 4318, 35068, 299907, 2668994, 24513578, 230981316, 2222973742, 21777680644, 216603095388, 2182653550712, 22245324259811, 228995136248850, 2378208988952434, 24893925007653748, 262424206657706682, 2784074166633171596, 29707452318776988260, 318664451642694840264
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: 54*z/(1+36*z-(1-12*z)^(3/2)) [Cervetti-Ferrari]. - N. J. A. Sloane, Nov 30 2020
Special values of the hypergeometric function 2F1, in Maple notation: a(n) = (27/8)*doublefactorial(2*n-1)*6^n*hypergeom([2, n+1/2], [n+3], -3)/(n+2)!, n>0. - Karol A. Penson and Wojciech Mlotkowski, Aug 04 2013
D-finite with recurrence n*a(n) +2*(-4*n+17)*a(n-1) +24*(-2*n+3)*a(n-2)=0. - R. J. Mathar, Aug 04 2013
G.f.: ((1-12*x)^(3/2) + (1+36*x)) / (2*(4*x+1)^2). - Vaclav Kotesovec, Aug 23 2014
a(n) ~ 2^(2*n-7) * 3^(n+3) / (sqrt(Pi) * n^(5/2)). - Vaclav Kotesovec, Aug 23 2014
G.f. A(x) satisifies A(x) = 1 + x*A(x)^2*(2 - G(x*A(x)^2))*G(x*A(x)^2)^2, where G(x) = 1 + x*G(x)^4 is the g.f. of A002293. - Paul D. Hanna, Aug 25 2014
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MATHEMATICA
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CoefficientList[Series[((1-12*x)^(3/2) + (1+36*x)) / (2*(4*x+1)^2), {x, 0, 20}], x] (* Vaclav Kotesovec, Aug 23 2014 *)
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PROG
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(PARI) x='x+O('x^50); Vec(((1-12*x)^(3/2)+(1+36*x))/(2*(4*x+1)^2)) \\ Altug Alkan, Nov 25 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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