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A112699
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Partial sum of Catalan numbers A000108 multiplied by powers of 5.
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1
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1, 6, 56, 681, 9431, 140681, 2203181, 35718806, 594312556, 10090406306, 174113843806, 3044524000056, 53828703687556, 960689055250056, 17284175383375056, 313147365080640681, 5708299647795484431
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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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a(n) = Sum_{k=0,..,n} C(k)*5^k, n>=0, with C(n):=A000108(n).
G.f.: c(5*x)/(1-x), where c(x):=(1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers A000108.
Recurrence: (n+1)*a(n) = 3*(7*n-3)*a(n-1) - 10*(2*n-1)*a(n-2). - Vaclav Kotesovec, Oct 19 2012
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MATHEMATICA
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CoefficientList[Series[(1-Sqrt[1-20*x])/(10*x)/(1-x), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)
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PROG
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(PARI) x='x+O('x^50); Vec((1-sqrt(1-20*x))/(10*x*(1-x))) \\ G. C. Greubel, Mar 17 2017
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CROSSREFS
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Sixth column (m=5) of triangle A112705.
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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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