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A210496
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Number of set partitions of [n] avoiding the patterns {1123, 1211}.
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1
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1, 1, 2, 5, 13, 33, 81, 196, 470, 1126, 2699, 6487, 15633, 37788, 91589, 222572, 542145, 1323446, 3237074, 7932108, 19469151, 47860083, 117819348, 290424126, 716772644, 1771035921, 4380646788, 10846386691, 26880759090, 66678169061, 165534924098, 411281773379, 1022621256416, 2544478797575, 6335428289930, 15784538365081, 39350771601502, 98158461390807
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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.: ( (1-x^2)*sqrt((1-x)*(1-x-4*x^2)) -(1-3*x-2*x^2 +14*x^3 -15*x^4 +3*x^5) / (1-x)^2 ) / ( 2*x^2*(1-3*x+x^2) ).
a(n) ~ sqrt((5389+1307*sqrt(17))/2)*((1+sqrt(17))/2)^n/(n^(3/2)*sqrt(Pi)). - Vaclav Kotesovec, Jul 30 2013
Conjecture: (n+2)*a(n) +2*(-3*n-4)*a(n-1) +4*(2*n+3)*a(n-2) +(13*n-40)*a(n-3) +5*(-7*n+18)*a(n-4) +6*(2*n-1)*a(n-5) +22*(n-7)*a(n-6) +(-19*n+134)*a(n-7) +2*(2*n-15)*a(n-8)=0. - R. J. Mathar, Oct 08 2016
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MATHEMATICA
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CoefficientList[Series[((1-x^2)*Sqrt[(1-x)*(1-x-4*x^2)]-(1-3*x-2*x^2 +14*x^3-15*x^4+3*x^5)/(1-x)^2)/(2*x^2*(1-3*x+x^2)), {x, 0, 20}], x]
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PROG
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(PARI) x='x+O('x^50); Vec(( (1-x^2)*sqrt((1-x)*(1-x-4*x^2)) -(1-3*x-2*x^2+14*x^3-15*x^4+3*x^5) / (1-x)^2 ) / ( 2*x^2*(1-3*x+x^2) )) \\ G. C. Greubel, May 31 2017
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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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