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A097141
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Expansion of x*(1+2*x)/(1+x)^2.
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4
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0, 1, 0, -1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15, 16, -17, 18, -19, 20, -21, 22, -23, 24, -25, 26, -27, 28, -29, 30, -31, 32, -33, 34, -35, 36, -37, 38, -39, 40, -41, 42, -43, 44, -45, 46, -47, 48, -49, 50, -51, 52, -53, 54, -55, 56, -57, 58, -59, 60
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OFFSET
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0,5
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COMMENTS
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Binomial transform is x(1+x)/(1-x), or {0,1,2,2,2,2,....}.
Second binomial transform is x/((1-x)^2(1 - 2x)), or Eulerian numbers A000295(n+1).
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LINKS
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FORMULA
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G.f.: x*(1+2*x)/(1+x)^2.
a(n) = (n-2)*(-1)^n + 2*0^n.
a(n) = -2*a(n-1) - a(n-2) for n > 2.
a(n) = (Sum_{k=1..n} k*(-1)^(n-k)*binomial(n-1,k-1)*binomial(2*n-k-1,n-1))/n, n>0, a(0)=0. - Vladimir Kruchinin, Mar 09 2014
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MAPLE
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MATHEMATICA
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CoefficientList[Series[x (1 + 2 x)/(1 + x)^2, {x, 0, 100}], x] (* Vincenzo Librandi, Mar 11 2014 *)
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PROG
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(Magma) [0] cat [(n-2)*(-1)^n : n in [1..100]]; // Wesley Ivan Hurt, Dec 11 2016
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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