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Search: id:A113070
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| A113070 |
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Expansion of ((1+x)/(1-2x))^2. |
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+0
2
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| 1, 6, 21, 60, 156, 384, 912, 2112, 4800, 10752, 23808, 52224, 113664, 245760, 528384, 1130496, 2408448, 5111808, 10813440, 22806528, 47972352, 100663296, 210763776, 440401920, 918552576, 1912602624, 3976200192, 8254390272, 17112760320
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OFFSET
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0,2
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COMMENT
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Binomial transform is A014915. 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
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G.f.: (1+x)^2/(1-2x)^2; a(n)=3*2^n(3n+1)/4+0^n/4; a(n)=sum{k=0..n, A003945(k)A003945(n-k)}; a(n)=sum{k=0..n, C(n, k)*sum{j=0..k, (j+1)*3^j}}.
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CROSSREFS
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Cf. A113071.
Sequence in context: A047520 A143115 A066524 this_sequence A009147 A012593 A048476
Adjacent sequences: A113067 A113068 A113069 this_sequence A113071 A113072 A113073
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 14 2005
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