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%I #17 Nov 26 2021 12:57:34
%S 1,1,1,1,6,1,1,19,19,1,1,48,126,48,1,1,109,594,594,109,1,1,234,2367,
%T 4812,2367,234,1,1,487,8565,31203,31203,8565,487,1,1,996,29188,176412,
%U 312310,176412,29188,996,1,1,2017,95644,910300,2620582,2620582,910300
%N Triangle t(n,m) = 2*A008292(n+1,m+1) - A007318(n,m), a linear combination of Eulerian numbers and Pascal's triangle, 0 <= m <= n.
%C Row sums are 1, 2, 8, 40, 224, 1408, 10016, 80512, 725504, 7257088, ... = 2*(n+1)! - 2^n.
%H G. C. Greubel, <a href="/A141690/b141690.txt">Rows n = 0..100 of triangle, flattened</a>
%e Triangle begins
%e 1;
%e 1, 1;
%e 1, 6, 1;
%e 1, 19, 19, 1;
%e 1, 48, 126, 48, 1;
%e 1, 109, 594, 594, 109, 1;
%e 1, 234, 2367, 4812, 2367, 234, 1;
%e 1, 487, 8565, 31203, 31203, 8565, 487, 1;
%e 1, 996, 29188, 176412, 312310, 176412, 29188, 996, 1;
%e 1, 2017, 95644, 910300, 2620582, 2620582, 910300, 95644, 2017, 1;
%p A141690 := proc(n,m)
%p 2*A008292(n+1,m+1)-binomial(n,m) ;
%p end proc: # _R. J. Mathar_, Jul 12 2012
%t Table[Table[(2*Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}] - Binomial[n - 1, k]), {k, 0, n - 1}], {n, 1, 10}]; Flatten[%]
%Y Cf. A008292, A007318.
%K nonn,tabl
%O 0,5
%A _Roger L. Bagula_, Sep 09 2008
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