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A176489 Triangle T(n,k) = A176487(n,k)+A176488(n,k)-1 read by rows 0<=k<=n.

%I A176489 #8 Jun 17 2015 04:00:34
%S A176489 1,1,1,1,12,1,1,35,35,1,1,82,206,82,1,1,177,922,922,177,1,1,368,3599,
%T A176489 7284,3599,368,1,1,751,12917,46923,46923,12917,751,1,1,1518,43876,
%U A176489 264810,468706,264810,43876,1518,1,1,3053,143588,1365740,3931310
%N A176489 Triangle T(n,k) = A176487(n,k)+A176488(n,k)-1 read by rows 0<=k<=n.
%C A176489 Row sums are 1, 2, 14, 72, 372, 2200, 15220, 121184, 1089116, 10887384, 119752404,....
%C A176489 The row sums s(n) seem to obey (-45*n+124)*s(n) +(45*n^2+127*n-654)*s(n-1) +(-206*n^2+227*n+708)*s(n-2) +(303*n^2-869*n+458)*s(n-3) -2*(71*n-125)*(n-2)*s(n-4)=0. - _R. J. Mathar_, Jun 16 2015
%e A176489 1;
%e A176489 1, 1;
%e A176489 1, 12, 1;
%e A176489 1, 35, 35, 1;
%e A176489 1, 82, 206, 82, 1;
%e A176489 1, 177, 922, 922, 177, 1;
%e A176489 1, 368, 3599, 7284, 3599, 368, 1;
%e A176489 1, 751, 12917, 46923, 46923, 12917, 751, 1;
%e A176489 1, 1518, 43876, 264810, 468706, 264810, 43876, 1518, 1;
%e A176489 1, 3053, 143588, 1365740, 3931310, 3931310, 1365740, 143588, 3053, 1;
%e A176489 1, 6124, 457997, 6610700, 29214758, 47173244, 29214758, 6610700, 457997, 6124, 1;
%p A176489 A176489 := proc(n,k)
%p A176489     A176487(n,k)+A176488(n,k)-1 ;
%p A176489 end proc: # _R. J. Mathar_, Jun 16 2015
%t A176489 << DiscreteMath`Combinatorica`;
%t A176489 t[n_, m_, 0] := Binomial[n, m];
%t A176489 t[n_, m_, 1] := Eulerian[1 + n, m];
%t A176489 t[n_, m_, q_] := t[n, m, q] = t[n, m, q - 1] + t[n, m, q - 2] - 1;
%t A176489 Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]
%Y A176489 Cf. A007318, A008292.
%K A176489 nonn,tabl,easy
%O A176489 0,5
%A A176489 _Roger L. Bagula_, Apr 19 2010