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A162482
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Expansion of (1/(1-x)^3)*M(x/(1-x)^3), M(x) the g.f. of Motzkin numbers A001006.
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2
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1, 4, 14, 53, 218, 945, 4235, 19441, 90947, 432030, 2078416, 10105435, 49578341, 245131321, 1220218293, 6110131376, 30756858405, 155547919269, 789965192900, 4027121386190, 20600180351659, 105707046807196, 543973305719611
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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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G.f.: 1/((1-x)^3-x-x^2/((1-x)^3-x-x^2/((1-x)^3-x-x^2/((1-x)^3-x-x^2/(1-... (continued fraction);
a(n) = sum{k=0..n, C(n+2k+2,n-k)*A001006(k)}.
Conjecture: (n+2)*a(n) +4*(-2*n-1)*a(n-1) +18*(n-1)*a(n-2) +13*(-2*n+5)*a(n-3) +17*(n-4)*a(n-4) +3*(-2*n+11)*a(n-5) +(n-7)*a(n-6)=0. - R. J. Mathar, Feb 10 2015
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MAPLE
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add(binomial(n+2*k+2, n-k)*A001006(k), k=0..n) ;
end proc:
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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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