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A124844 Triangle T(n,k)=binomial(n,k)*A061084(k), 0<=k<=n, read by rows.

%I A124844 #9 Sep 15 2015 10:20:49
%S A124844 1,1,2,1,4,-1,1,6,-3,3,1,8,-6,12,-4,1,10,-10,30,-20,7,1,12,-15,60,-60,
%T A124844 42,-11,1,14,-21,105,-140,147,-77,18,1,16,-28,168,-280,392,-308,144,
%U A124844 -29,1,18,-36,252,-504,882,-924,648,-261,47,1,20,-45,360,-840,1764,-2310,2160,-1305,470,-76
%N A124844 Triangle T(n,k)=binomial(n,k)*A061084(k), 0<=k<=n, read by rows.
%H A124844 Reinhard Zumkeller, <a href="/A124844/b124844.txt">Rows n = 0..125 of triangle, flattened</a>
%F A124844 We let A061084 = the diagonal of an infinite matrix, M. Perform P*M and extract the zeros, where P = Pascal's triangle as an infinite lower triangular matrix.
%e A124844 First few rows of the triangle are:
%e A124844 1;
%e A124844 1, 2;
%e A124844 1, 4, -1;
%e A124844 1, 6, -3, 3;
%e A124844 1, 8, -6, 12, -4;
%e A124844 1, 10, -10, 30, -20, 7;
%e A124844 1, 12, -15, 60, -60, 42, -11;
%e A124844 1, 14, -21, 105, -140, 147, -77, 18;
%e A124844 ...
%o A124844 (Haskell)
%o A124844 import Data.List (inits)
%o A124844 a124844 n k = a124844_tabl !! n !! k
%o A124844 a124844_row n = a124844_tabl !! n
%o A124844 a124844_tabl = zipWith (zipWith (*))
%o A124844                        a007318_tabl $ tail $ inits a061084_list
%o A124844 -- _Reinhard Zumkeller_, Sep 15 2015
%Y A124844 Cf. A061084, A000032, A000204 (row sums).
%Y A124844 Cf. A007318.
%K A124844 sign,easy,tabl
%O A124844 0,3
%A A124844 _Gary W. Adamson_, Nov 10 2006