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A073155
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Leftmost column sequence of triangle A073153.
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14
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1, 1, 4, 14, 56, 237, 1046, 4762, 22198, 105430, 508384, 2482297, 12248416, 60980875, 305955356, 1545397464, 7852100294, 40105277640, 205798130604, 1060467961508, 5485199090812, 28469067353686, 148220323891460
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OFFSET
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0,3
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LINKS
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FORMULA
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Convolution of sequence formed from sum of adjacent terms yields the original sequence without the first term:
a(n+1) = Sum_{k=0..n} [a(k) + a(k-1)] * [a(n-k) + a(n-k-1)], where a(-1)=0.
G.f.: 1/2*(1-(1-4*x*(1+x)^2)^(1/2))/x/(1+x)^2. - Vladeta Jovovic, Oct 10 2003
a(n) = Sum_{k=0..n} C(2k,n-k)*C(k). - Paul Barry, Jul 09 2006
Conjecture: (n+1)*a(n) + (-3*n+4)*a(n-1) + 2*(-6*n+7)*a(n-2) + 2*(-6*n+11)*a(n-3) + 2*(-2*n+5)*a(n-4)=0. - R. J. Mathar, Nov 26 2012
G.f. A(x) satisfies: A(x) = 1 + x * ((1 + x) * A(x))^2. - Ilya Gutkovskiy, Jul 10 2020
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EXAMPLE
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a(3)=a(0)*[a(2)+a(1)]+[a(1)+a(0)]*[a(1)+a(0)]+[a(2)+a(1)]*a(0) =1*[4+1] + [1+1]*[1+1] + [4+1]*1 = 5 + 2*2 + 5 = 14.
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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