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A081908
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a(n) = 2^n*(n^2 - n + 8)/8.
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6
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1, 2, 5, 14, 40, 112, 304, 800, 2048, 5120, 12544, 30208, 71680, 167936, 389120, 892928, 2031616, 4587520, 10289152, 22937600, 50855936, 112197632, 246415360, 538968064, 1174405120, 2550136832, 5519704064, 11911823360, 25635586048
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A000124 (when this begins 1,1,2,4,7,...).
2nd binomial transform of (1,0,1,0,0,0,...).
Case k=2 where a(n,k) = k^n(n^2 - n + 2k^2)/(2k^2) with g.f. (1 - 2kx + (k^2+1)x^2)/(1-kx)^3.
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LINKS
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FORMULA
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G.f.: (1 - 4*x + 5*x^2)/(1-2*x)^3.
a(n) = Sum_{k=0..n} C(n, k)*(1 + C(k, 2)). - Paul Barry, May 27 2003
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MATHEMATICA
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Table[2^n*(n^2-n+8)/8, {n, 0, 50}] (* or *) LinearRecurrence[{6, -12, 8}, {1, 2, 5}, 50] (* G. C. Greubel, Oct 17 2018 *)
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PROG
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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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STATUS
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approved
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