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%I #2 Mar 30 2012 17:34:27
%S 1,1,1,1,5,1,1,15,15,1,1,37,96,37,1,1,83,448,448,83,1,1,177,1779,3614,
%T 1779,177,1,1,367,6429,23411,23411,6429,367,1,1,749,21898,132323,
%U 234250,132323,21898,749,1,1,1515,71742,682746,1965468,1965468,682746,71742
%N A linear combination of Eulerian numbers (A008292) and Pascal's triangle (A007318); t(n,m)=(3*A008292(n,m)-A007318(n,m))/2.
%C Row sums are:
%C {1, 2, 7, 32, 172, 1064, 7528, 60416, 544192, 5442944}.
%F t(n,m)=(3*A008292(n,m)-A007318(n,m))/2.
%e {1},
%e {1, 1},
%e {1, 5, 1},
%e {1, 15, 15, 1},
%e {1, 37, 96, 37, 1},
%e {1, 83, 448, 448, 83, 1},
%e {1, 177, 1779, 3614, 1779, 177, 1},
%e {1, 367, 6429, 23411, 23411, 6429, 367, 1},
%e {1, 749, 21898, 132323, 234250, 132323, 21898, 749, 1},
%e {1, 1515, 71742, 682746, 1965468, 1965468, 682746, 71742, 1515, 1}
%t Table[Table[((2*Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}] - Binomial[n - 1, k]) + Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}])/2, {k, 0, n - 1}], {n, 1, 10}]; Flatten[%]
%Y Cf. A008292, A007318.
%K nonn,uned
%O 1,5
%A _Roger L. Bagula_, Sep 09 2008
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