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 A084610 Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1+x-x^2)^n. 11

%I

%S 1,1,1,-1,1,2,-1,-2,1,1,3,0,-5,0,3,-1,1,4,2,-8,-5,8,2,-4,1,1,5,5,-10,

%T -15,11,15,-10,-5,5,-1,1,6,9,-10,-30,6,41,-6,-30,10,9,-6,1,1,7,14,-7,

%U -49,-14,77,29,-77,-14,49,-7,-14,7,-1,1,8,20,0,-70,-56,112,120,-125,-120,112,56,-70,0,20,-8,1,1,9,27,12,-90,-126,126,288

%N Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1+x-x^2)^n.

%H Paul D. Hanna, <a href="/A084610/b084610.txt">Rows n=0..34 of triangle, flattened</a>

%F G.f.: G(0)/2 , where G(k)= 1 + 1/( 1 - (1+x-x^2)*x^(2*k+1)/((1+x-x^2)*x^(2*k+1) + 1/G(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Jul 06 2013

%e Rows:

%e {1},

%e {1,1,-1},

%e {1,2,-1,-2,1},

%e {1,3,0,-5,0,3,-1},

%e {1,4,2,-8,-5,8,2,-4,1},

%e {1,5,5,-10,-15,11,15,-10,-5,5,-1},

%e {1,6,9,-10,-30,6,41,-6,-30,10,9,-6,1},

%e {1,7,14,-7,-49,-14,77,29,-77,-14,49,-7,-14,7,-1},

%o (PARI) for(n=0,12, for(k=0,2*n,t=polcoeff((1+x-x^2)^n,k,x); print1(t",")); print(" "))

%Y Cf. A002426, A084600-A084609, A084611-A084615.

%K sign,tabf

%O 0,6

%A _Paul D. Hanna_, Jun 01 2003

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Last modified August 22 16:17 EDT 2019. Contains 326178 sequences. (Running on oeis4.)