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A114211
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Expansion of (1+6x^2-2x^3)/(1-x)^4.
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0
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1, 4, 16, 42, 87, 156, 254, 386, 557, 772, 1036, 1354, 1731, 2172, 2682, 3266, 3929, 4676, 5512, 6442, 7471, 8604, 9846, 11202, 12677, 14276, 16004, 17866, 19867, 22012, 24306, 26754, 29361, 32132, 35072, 38186, 41479
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Column 3 of A114202. Third differences are 1,1,7,5,5,5,5,5,... with g.f. (1+6x^2-2x^3)/(1-x).
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FORMULA
| G.f.: (1+3(x/(1-x))+9(x/(1-x))^2+5(x/(1-x))^3)/(1-x); a(n)=sum{k=0..n, C(n, k)C(3, k)J(k+1)}, J(n)=A001045(n); a(0)=1, a(n)=a(n-1)+(n-1)(n+2)+A104249(n).
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EXAMPLE
| [1,3,9,5]=[1*1,3*1,3*3,1*5]=[C(3,0)*J(1),C(3,1)*J(2),C(3,2)*J(3),C(3,3)*J(4)].
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MATHEMATICA
| CoefficientList[Series[(1+6x^2-2x^3)/(1-x)^4, {x, 0, 75}], x] (* From Harvey P. Dale, Mar 6 2011 *)
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CROSSREFS
| Sequence in context: A007057 A056373 A018828 * A188124 A190090 A034131
Adjacent sequences: A114208 A114209 A114210 * A114212 A114213 A114214
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Nov 17 2005
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