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A097749 Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows. Let A(n,k) be the triangle in A097474. Then T(n,k) is defined by the orthogonality relations Sum_{j=i..r} T(r,j)*A(j,i)*2^-floor((j+3)/2) = 0 if i != r, = (2r+1)!/(r!*2^r) if i = r.

%I A097749 #6 Mar 25 2013 19:51:30
%S A097749 2,1,2,-1,10,6,5,-35,105,30,-63,420,-882,1260,210,1576,-10395,20790,
%T A097749 -20790,17325,1890,-68409,450450,-891891,849420,-495495,270270,20790,
%U A097749 4729726,-31126095,61486425,-57972915,32207175,-12297285,4729725,270270
%N A097749 Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows. Let A(n,k) be the triangle in A097474. Then T(n,k) is defined by the orthogonality relations Sum_{j=i..r} T(r,j)*A(j,i)*2^-floor((j+3)/2) = 0 if i != r, = (2r+1)!/(r!*2^r) if i = r.
%D A097749 H. W. Gould, Power sum identities for arbitrary symmetric arrays, SIAM J. Appl. Math., 17 (1969), 307-316.
%e A097749 Triangle begins:
%e A097749 2
%e A097749 1 2
%e A097749 -1 10 6
%e A097749 5 -35 105 30
%e A097749 -63 420 -882 1260 210
%Y A097749 Cf. A097474, A097801. Row sums give A001147. Is the left-hand edge A004193?
%K A097749 sign,tabl,easy
%O A097749 0,1
%A A097749 _N. J. A. Sloane_, Sep 21 2004
%E A097749 More terms from _Sean A. Irvine_, Mar 25 2013