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A111997
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Ninth convolution of Schroeder's (second problem) numbers A001003(n), n>=0.
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1
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1, 9, 63, 399, 2403, 14067, 80949, 460845, 2605590, 14666470, 82320714, 461238282, 2581644378, 14442658074, 80785970838, 451934259654, 2528977211775, 14157983986839, 79302044283297, 444448115168049, 2492468172937125
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OFFSET
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0,2
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
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FORMULA
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G.f.: ((1+x-sqrt(1-6*x+x^2))/(4*x))^9.
a(n) = (9/n)*Sum_{k=1,..,n} binomial(n,k)*binomial(n+k+8,k-1).
a(n) = 9*hypergeom([1-n, n+10], [2], -1), n>=1, a(0)=1.
Recurrence: n*(n+9)*a(n) = (7*n^2+51*n+32)*a(n-1) - (7*n^2+33*n-22)*a(n-2) + (n-3)*(n+6)*a(n-3). - Vaclav Kotesovec, Oct 18 2012
a(n) ~ 9*sqrt(3*sqrt(2)-4)*(577-408*sqrt(2)) * (3+2*sqrt(2))^(n+9)/(64*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 18 2012
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MATHEMATICA
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CoefficientList[Series[((1+x-Sqrt[1-6*x+x^2])/(4*x))^9, {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 18 2012 *)
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PROG
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(PARI) x='x+O('x^50); Vec(((1+x-sqrt(1-6*x+x^2))/(4*x))^9) \\ G. C. Greubel, Mar 17 2017
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CROSSREFS
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Ninth column of convolution triangle A011117.
Sequence in context: A073378 A316461 A022733 * A016137 A230547 A339786
Adjacent sequences: A111994 A111995 A111996 * A111998 A111999 A112000
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Sep 12 2005
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STATUS
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approved
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