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A056126
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a(n) = n*(n + 17)/2.
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21
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0, 9, 19, 30, 42, 55, 69, 84, 100, 117, 135, 154, 174, 195, 217, 240, 264, 289, 315, 342, 370, 399, 429, 460, 492, 525, 559, 594, 630, 667, 705, 744, 784, 825, 867, 910, 954, 999, 1045, 1092, 1140, 1189, 1239, 1290, 1342, 1395, 1449, 1504, 1560, 1617, 1675
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: x*(9-8*x)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
If we define f(n,i,a) = Sum_{k=0..n-i} binomial(n,k)*stirling1(n-k,i)* Product_{j=0..k-1} (-a-j), then a(n) = -f(n,n-1,9), for n>=1. - Milan Janjic, Dec 20 2008
Sum_{n>=1} 1/a(n) = 2*A001008(17)/(17*A002805(17)) = 42142223/104144040.
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/17 - 1768477/20828808. (End)
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MAPLE
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MATHEMATICA
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PROG
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(Magma) [n*(n+17)/2: n in [0..50]]; // G. C. Greubel, Jan 19 2020
(Sage) [n*(n+17)/2 for n in (0..50)] # G. C. Greubel, Jan 19 2020
(GAP) List([0..50], n-> n*(n+17)/2 ); # G. C. Greubel, Jan 19 2020
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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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