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A127894 Inverse of Riordan array (1/(1-x)^3, x/(1-x)^3). 2

%I

%S 1,-3,1,12,-6,1,-55,33,-9,1,273,-182,63,-12,1,-1428,1020,-408,102,-15,

%T 1,7752,-5814,2565,-760,150,-18,1,-43263,33649,-15939,5313,-1265,207,

%U -21,1,246675,-197340,98670,-35880,9750,-1950,273,-24,1

%N Inverse of Riordan array (1/(1-x)^3, x/(1-x)^3).

%C First column is (-1)^n*A001764(n+1). Row sums are (-1)^n*A006013(n). Inverse of A127893.

%H G. C. Greubel, <a href="/A127894/b127894.txt">Rows n=0..100 of triangle, flattened</a>

%e Triangle begins

%e 1,

%e -3, 1,

%e 12, -6, 1,

%e -55, 33, -9, 1,

%e 273, -182, 63, -12, 1,

%e -1428, 1020, -408, 102, -15, 1,

%e 7752, -5814, 2565, -760, 150, -18, 1,

%e -43263, 33649, -15939, 5313, -1265, 207, -21, 1,

%e 246675, -197340, 98670, -35880, 9750, -1950, 273, -24, 1,

%e -1430715, 1170585, -610740, 237510, -71253, 16443, -2842, 348, -27, 1,

%e 8414640, -7012200, 3786588, -1553472, 503440, -129456, 26040, -3968, 432, -30, 1

%t Table[If[k == 0, (-1)^(n-1)*Binomial[3*n, n-k]/(2*n+1), (-1)^(n-k-1)*((k + 1)/(n))*Binomial[3*n, n-k-1]], {n, 1, 100}, {k, 0, n-1}] // Flatten (* _G. C. Greubel_, Apr 29 2018 *)

%o (PARI) for(n=1,10, for(k=0,n-1, print1(if(k==0, (-1)^(n-1)*binomial(3*n, n-k)/(2*n+1), (-1)^(n-k-1)*((k+1)/n)*binomial(3*n, n-k-1)), ", "))) \\ _G. C. Greubel_, Apr 29 2018

%Y Cf. A001764, A006013, A127893.

%K sign,tabl

%O 0,2

%A _Paul Barry_, Feb 04 2007

%E Terms a(39) onward added by _G. C. Greubel_, Apr 29 2018

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Last modified June 24 06:17 EDT 2021. Contains 345416 sequences. (Running on oeis4.)