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A126221
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a(n)=c(n)+c(n-1)+2*c(n-2)+4*c(n-3)+8*c(n-4)+...+2^(n-2)*c(1)+2^(n-1)*c(0), where c(k) are the Catalan numbers (A000108).
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1
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1, 2, 5, 13, 35, 98, 286, 869, 2739, 8910, 29754, 101498, 352222, 1239332, 4410204, 15840813, 57344451, 208976022, 765945954, 2821516398, 10439890026, 38781926652, 144580149924, 540737349858, 2028319233390, 7628680720908
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OFFSET
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0,2
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COMMENTS
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Equals the eigensequence of a triangle with A000108 as the left border and the rest 1's. - Gary W. Adamson, Jul 24 2010
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LINKS
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FORMULA
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G.f.: (1-x)*(1-sqrt(1-4*x)) / (2*x*(1-2*x)).
D-finite with recurrence (n+1)*a(n) +(-7*n+1)*a(n-1) +2*(7*n-8)*a(n-2) +4*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Jul 22 2022
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EXAMPLE
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a(4)=35 because c(4)+c(3)+2*c(2)+4*c(1)+8*c(0) = 14+5+2*2+4*1+8*1 = 35.
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MAPLE
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c:=n->binomial(2*n, n)/(n+1): a:=n->c(n)+sum(2^(n-j-1)*c(j), j=0..n-1): seq(a(n), n=0..30);
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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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