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%I #9 Jun 17 2015 03:59:17
%S 1,1,1,1,8,1,1,23,23,1,1,54,136,54,1,1,117,612,612,117,1,1,244,2395,
%T 4850,2395,244,1,1,499,8605,31271,31271,8605,499,1,1,1010,29242,
%U 176522,312448,176522,29242,1010,1,1,2033,95714,910466,2620832,2620832,910466
%N Triangle T(n,k) = A008292(n+1,k+1) + A176487(n,k) - 1, 0<=k<=n.
%C Row sums are 1, 2, 10, 48, 246, 1460, 10130, 80752, 725998, 7258092, 79834602,....
%C Apparently the row sums 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 1;
%e 1, 1;
%e 1, 8, 1;
%e 1, 23, 23, 1;
%e 1, 54, 136, 54, 1;
%e 1, 117, 612, 612, 117, 1;
%e 1, 244, 2395, 4850, 2395, 244, 1;
%e 1, 499, 8605, 31271, 31271, 8605, 499, 1;
%e 1, 1010, 29242, 176522, 312448, 176522, 29242, 1010, 1;
%e 1, 2033, 95714, 910466, 2620832, 2620832, 910466, 95714, 2033, 1;
%e 1, 4080, 305317, 4407094, 19476436, 31448746, 19476436, 4407094, 305317, 4080, 1;
%p A176488 := proc(n,k)
%p A008292(n+1,k+1)+A176487(n,k)-1 ;
%p end proc: # _R. J. Mathar_, Jun 16 2015
%t << DiscreteMath`Combinatorica`;
%t t[n_, m_, 0] := Binomial[n, m];
%t t[n_, m_, 1] := Eulerian[1 + n, m];
%t t[n_, m_, q_] := t[n, m, q] = t[n, m, q - 1] + t[n, m, q - 2] - 1;
%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]
%Y Cf. A007318, A008292.
%K nonn,tabl,easy
%O 0,5
%A _Roger L. Bagula_, Apr 19 2010
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