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%I #14 Sep 08 2022 08:45:30
%S 1,0,2,-1,2,3,-2,0,6,4,-3,-4,6,12,5,-4,-10,0,20,20,6,-5,-18,-15,20,45,
%T 30,7,-6,-28,-42,0,70,84,42,8,-7,-40,-84,-56,70,168,140,56,9,-8,-54,
%U -144,-168,0,252,336,216,72,10
%N Binomial transform of A128064.
%C A128064 * A007318 = A103406 row sums = 2^(n-1).
%F A007318 * A128064 as infinite lower triangular matrices.
%e First few rows of the triangle are:
%e 1;
%e 0, 2;
%e -1, 2, 3;
%e -2, 0, 6, 4;
%e -3, -4, 6, 12, 5;
%e ...
%t Table[(k + 1) (Binomial[n, k] - Binomial[n, k + 1]), {n, 0,
%t 12}, {k, 0, n}] // Flatten (* _Nathaniel MacFadden_, Jul 11 2019 *)
%o (Magma) /* As triangle */ [[(k+1)*(Binomial(n,k)-Binomial(n,k+1)): k in [0..n]]: n in [0.. 15]]; // _Vincenzo Librandi_, Jul 12 2019
%Y Cf. A128064, A103406.
%K tabl,sign
%O 1,3
%A _Gary W. Adamson_, Feb 14 2007
%E a(43) corrected by _Nathaniel MacFadden_, Jul 11 2019
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