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A176492 Triangle T(n,k) = A176492(n,k) + A008292(n+1,k+1) - 1 read along rows 0<=k<=n.

%I A176492 #10 Jun 17 2015 04:04:43
%S A176492 1,1,1,1,13,1,1,45,45,1,1,129,365,129,1,1,353,2293,2293,353,1,1,965,
%T A176492 12937,28397,12937,965,1,1,2677,69261,290993,290993,69261,2677,1,1,
%U A176492 7561,360853,2661809,4987461,2661809,360853,7561,1,1,21705,1852053,22618437
%N A176492 Triangle T(n,k) = A176492(n,k) + A008292(n+1,k+1) - 1 read along rows 0<=k<=n.
%C A176492 Row sums are 1, 2, 15, 92, 625, 5294, 56203, 725864, 11047909, 193052642, 3795725791,....
%e A176492 1;
%e A176492 1, 1;
%e A176492 1, 13, 1;
%e A176492 1, 45, 45, 1;
%e A176492 1, 129, 365, 129, 1;
%e A176492 1, 353, 2293, 2293, 353, 1;
%e A176492 1, 965, 12937, 28397, 12937, 965, 1;
%e A176492 1, 2677, 69261, 290993, 290993, 69261, 2677, 1;
%e A176492 1, 7561, 360853, 2661809, 4987461, 2661809, 360853, 7561, 1;
%e A176492 , 21705, 1852053, 22618437, 72034125, 72034125, 22618437, 1852053, 21705, 1;
%e A176492 1, 63117, 9421457, 182707997, 926399717, 1558541213, 926399717, 182707997, 9421457, 63117, 1;
%p A176492 A176492 := proc(n,k)
%p A176492     A176491(n,k)+A008292(n+1,k+1)-1 ;
%p A176492 end proc: # _R. J. Mathar_, Jun 16 2015
%t A176492 (*A060187*)
%t A176492 p[x_, n_] = (1 - x)^(n + 1)*Sum[(2*k + 1)^n*x^k, {k, 0, Infinity}];
%t A176492 f[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];
%t A176492 << DiscreteMath`Combinatorica`;
%t A176492 t[n_, m_, 0] := Binomial[n, m];
%t A176492 t[n_, m_, 1] := Eulerian[1 + n, m];
%t A176492 t[n_, m_, 2] := f[n, m];
%t A176492 t[n_, m_, q_] := t[n, m, q] = t[n, m, q - 2] + t[n, m, q - 3] - 1;
%t A176492 Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]
%Y A176492 Cf. A007318, A008292, A060187, A176487.
%K A176492 nonn,tabl,easy
%O A176492 0,5
%A A176492 _Roger L. Bagula_, Apr 19 2010