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A113071
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Expansion of ((1+x)/(1-3x))^2.
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2
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1, 8, 40, 168, 648, 2376, 8424, 29160, 99144, 332424, 1102248, 3621672, 11809800, 38263752, 123294312, 395392104, 1262703816, 4017693960, 12741829416, 40291730856, 127073920392, 399817944648, 1255242384360, 3933092804328
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform is A014916. In general, ((1+x)/(1-r*x))^2 expands to a(n)=((r+1)r^n((r+1)n+r-1)+0^n)/r^2, which is also a(n)=sum{k=0..n, C(n,k)*sum{j=0..k, (j+1)*(r+1)^j}}. This is the self-convolution of the coordination sequence for the infinite tree with valency r.
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FORMULA
| G.f.: (1+x^2)/(1-3x)^2; a(n)=8*3^n(2n+1)/9+0^n/9=4*3^n(4n+2)/9+0^n/9; a(n)=sum{k=0..n, A003946(k)A003946(n-k)}; a(n)=sum{k=0..n, C(n, k)*sum{j=0..k, (j+1)*4^j}}.
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CROSSREFS
| Sequence in context: A004405 A001789 A074412 * A006726 A165665 A000760
Adjacent sequences: A113068 A113069 A113070 * A113072 A113073 A113074
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 14 2005
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