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A128065 Binomial transform of A128064.

%I A128065 #14 Sep 08 2022 08:45:30
%S A128065 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 A128065 30,7,-6,-28,-42,0,70,84,42,8,-7,-40,-84,-56,70,168,140,56,9,-8,-54,
%U A128065 -144,-168,0,252,336,216,72,10
%N A128065 Binomial transform of A128064.
%C A128065 A128064 * A007318 = A103406 row sums = 2^(n-1).
%F A128065 A007318 * A128064 as infinite lower triangular matrices.
%e A128065 First few rows of the triangle are:
%e A128065    1;
%e A128065    0,  2;
%e A128065   -1,  2,  3;
%e A128065   -2,  0,  6,  4;
%e A128065   -3, -4,  6, 12,  5;
%e A128065   ...
%t A128065 Table[(k + 1) (Binomial[n, k] - Binomial[n, k + 1]), {n, 0,
%t A128065 12}, {k, 0, n}] // Flatten (* _Nathaniel MacFadden_, Jul 11 2019 *)
%o A128065 (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 A128065 Cf. A128064, A103406.
%K A128065 tabl,sign
%O A128065 1,3
%A A128065 _Gary W. Adamson_, Feb 14 2007
%E A128065 a(43) corrected by _Nathaniel MacFadden_, Jul 11 2019