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%I #9 May 10 2019 23:39:00
%S 1,1,1,1,6,1,1,23,23,1,1,76,254,76,1,1,237,2410,2410,237,1,1,722,
%T 22007,67740,22007,722,1,1,2179,198905,1851507,1851507,198905,2179,1,
%U 1,6552,1792492,50190504,151826374,50190504,1792492,6552,1,1,19673,16139204
%N Triangle T(n,m) = 2*A022167(n,m) - binomial(n, m), 0 <= m <= n, read by rows.
%C Row sums are 1, 2, 8, 48, 408, 5296, 113200, 4105184, 255805472, 27442457664, 5089653253824, ... = 2*A006117(n)-2^n.
%e Triangle begins
%e 1;
%e 1, 1;
%e 1, 6, 1;
%e 1, 23, 23, 1;
%e 1, 76, 254, 76, 1;
%e 1, 237, 2410, 2410, 237, 1;
%e 1, 722, 22007, 67740, 22007, 722, 1;
%e 1, 2179, 198905, 1851507, 1851507, 198905, 2179, 1;
%e 1, 6552, 1792492, 50190504, 151826374, 50190504, 1792492, 6552, 1;
%p A174527 := proc(n,k)
%p 2*A022167(n,k)-binomial(n,k) ;
%p end proc:
%p seq(seq(A174527(n,m),m=0..n),n=0..10) ; # _R. J. Mathar_, Nov 14 2011
%t c[n_, q_] = Product[1 - q^i, {i, 1, n}];
%t t[n_, m_, q_] = 2*c[n, q]/(c[m, q]*c[n - m, q]) - Binomial[n, m];
%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]
%Y Cf. A060187.
%K nonn,tabl
%O 0,5
%A _Roger L. Bagula_ and _Gary W. Adamson_, Mar 21 2010
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