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A032952
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Expansion of (1+x*C^4)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
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1
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1, 3, 11, 41, 152, 561, 2067, 7618, 28118, 104006, 385662, 1433797, 5344510, 19973085, 74827395, 281000430, 1057628550, 3989213610, 15077120010, 57092280570, 216579650664, 822991216746, 3132339521966, 11939881979076, 45577753704252, 174218415470092, 666795041653916
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OFFSET
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0,2
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LINKS
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FORMULA
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Recurrence: (n+5)*(19*n-8)*a(n) = (113*n^2+307*n-76)*a(n-1) - 2*(2*n-1)*(37*n+36)*a(n-2). - Vaclav Kotesovec, Oct 08 2012
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MATHEMATICA
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Table[SeriesCoefficient[(1+x*((1-(1-4*x)^(1/2))/(2*x))^4)*((1-(1-4*x)^(1/2))/(2*x))^2, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 08 2012 *)
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PROG
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(PARI) x='x+O('x^66); C=(1-(1-4*x)^(1/2))/(2*x); Vec( (1+x*C^4)*C^2 ) \\ Joerg Arndt, May 04 2013
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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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