%I #9 Jun 17 2015 04:03:49

%S 1,1,1,1,10,1,1,35,35,1,1,104,300,104,1,1,297,1992,1992,297,1,1,846,

%T 11747,25982,11747,846,1,1,2431,64969,275375,275375,64969,2431,1,1,

%U 7060,346246,2573576,4831272,2573576,346246,7060,1,1,20693,1804214,22163246

%N Triangle T(n,k) = binomial(n,k) + A176490(n,k) - 1 read along rows 0<=k<=n.

%C Row sums are 1, 2, 12, 72, 510, 4580, 51170, 685552, 10685038, 189423852, 3755809002,....

%e 1;

%e 1, 1;

%e 1, 10, 1;

%e 1, 35, 35, 1;

%e 1, 104, 300, 104, 1;

%e 1, 297, 1992, 1992, 297, 1;

%e 1, 846, 11747, 25982, 11747, 846, 1;

%e 1, 2431, 64969, 275375, 275375, 64969, 2431, 1;

%e 1, 7060, 346246, 2573576, 4831272, 2573576, 346246, 7060, 1;

%e 1, 20693, 1804214, 22163246, 70723772, 70723772, 22163246, 1804214, 20693, 1;

%e 1, 61082, 9268821, 180504510, 916661604, 1542816966, 916661604, 180504510, 9268821, 61082, 1;

%p A176491 := proc(n,k)

%p A176490(n,k)+binomial(n,k)-1 ;

%p end proc: # _R. J. Mathar_, Jun 16 2015

%t (*A060187*)

%t p[x_, n_] = (1 - x)^(n + 1)*Sum[(2*k + 1)^n*x^k, {k, 0, Infinity}];

%t f[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];

%t << DiscreteMath`Combinatorica`;

%t t[n_, m_, 0] := Binomial[n, m];

%t t[n_, m_, 1] := Eulerian[1 + n, m];

%t t[n_, m_, 2] := f[n, m];

%t t[n_, m_, q_] := t[n, m, q] = t[n, m, q - 2] + t[n, m, q - 3] - 1;

%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]

%Y Cf. A007318, A008292, A060187, A176487.

%K nonn,tabl,easy

%O 0,5

%A _Roger L. Bagula_, Apr 19 2010