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A062534 Table by antidiagonals of coefficient of x^k in expansion of 1/((1+x)^2*(1-x)^n). 1

%I

%S 1,-2,1,3,-1,1,-4,2,0,1,5,-2,2,1,1,-6,3,0,3,2,1,7,-3,3,3,5,3,1,-8,4,0,

%T 6,8,8,4,1,9,-4,4,6,14,16,12,5,1,-10,5,0,10,20,30,28,17,6,1,11,-5,5,

%U 10,30,50,58,45,23,7,1,-12,6,0,15,40,80,108,103,68,30,8,1,13,-6,6,15,55,120,188,211,171,98,38,9,1,-14,7,0,21,70,175

%N Table by antidiagonals of coefficient of x^k in expansion of 1/((1+x)^2*(1-x)^n).

%F Each row is partial sum of preceding row, i.e. T(n, k)=T(n-1, k)+T(n, k-1) with T(0, k)=(k+1)*(-1)^k and T(n, 0)=1.

%Y Rows are effectively (with minor adjustments): A038608, A001057, A027656, A008805, A006918, A002624, A028346. Cf. A058394 which (adjusting for signs and an overlap of three rows) is effectively the continuation of this table for negative n.

%K sign,tabl

%O 0,2

%A _Henry Bottomley_, Jun 25 2001

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Last modified August 10 07:37 EDT 2020. Contains 336368 sequences. (Running on oeis4.)