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A076036
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G.f.: 1/(1 - 5*x*C(x)), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) = g.f. for the Catalan numbers A000108.
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11
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1, 5, 30, 185, 1150, 7170, 44760, 279585, 1746870, 10916150, 68219860, 426353130, 2664633580, 16653699860, 104084695500, 650526003825, 4065775405350, 25411052086350, 158818913483700, 992617612224750, 6203857867325700, 38774103465635100, 242338116077385600
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OFFSET
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0,2
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COMMENTS
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Numbers have the same parity as the Catalan numbers, that is, a(n) is even except for n of the form 2^m - 1. Follows from C(x) = 1/(1 - x*C(x)) = 1/(1 - 5*x*C(x)) (mod 2). - Peter Bala, Jul 24 2016
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LINKS
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FORMULA
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D-finite with recurrence: +4*n*a(n) +(-41*n+24)*a(n-1) +50*(2*n-3)*a(n-2)=0. - R. J. Mathar, Jan 20 2020
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PROG
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(PARI) C(x) = (1 - sqrt(1 - 4*x))/(2*x);
my(x = 'x + O('x^25)); Vec(1/(1 - 5*x*C(x))) \\ Michel Marcus, Jan 21 2020
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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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