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Search: id:A114211
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| A114211 |
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Expansion of (1+6x^2-2x^3)/(1-x)^4. |
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+0
1
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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
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OFFSET
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0,2
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COMMENT
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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
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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
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[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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CROSSREFS
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Adjacent sequences: A114208 A114209 A114210 this_sequence A114212 A114213 A114214
Sequence in context: A007057 A056373 A018828 this_sequence A034131 A018210 A054498
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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), Nov 17 2005
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