%I A154915
%S A154915 4,3,3,5,8,5,9,24,24,9,17,70,112,70,17,33,198,480,480,198,33,65,544,
%T A154915 1920,2880,1920,544,65,129,1452,7308,15624,15624,7308,1452,129,257,3770,
%U A154915 26724,80640,108864,80640,26724,3770,257,513,9546,94644,408312,706608
%N A154915 A triangular sequence: p = 2; q = 1; t(n,m) = (p^(n - m)*q^m + p^m*q^( 
               n - m))*(StirlingS2[n, m] + StirlingS2[n, n - m]).
%C A154915 Row sums are:
%C A154915 {4, 6, 18, 66, 286, 1422, 7938, 49026, 331646, 2439246, 19394498,..}.
%C A154915 Fractal Plot:
%C A154915 a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 243}];
%C A154915 b = Table[If[m <= n, 3 - Mod[a[[n]][[m]], 3], 0], {m, 1, Length[a]}, 
               {n, 1, Length[a]}];
%C A154915 ListDensityPlot[b, Mesh -> False, Frame -> False, AspectRatio -> Automatic, 
               ColorFunction -> (Hue[2# ] &)]
%F A154915 p = 2; q = 1;
%F A154915 t(n,m) = (p^(n - m)*q^m + p^m*q^(n - m))*(StirlingS2[n, m] + StirlingS2[n, 
               n - m]).
%e A154915 {4},
%e A154915 {3, 3},
%e A154915 {5, 8, 5},
%e A154915 {9, 24, 24, 9},
%e A154915 {17, 70, 112, 70, 17},
%e A154915 {33, 198, 480, 480, 198, 33},
%e A154915 {65, 544, 1920, 2880, 1920, 544, 65},
%e A154915 {129, 1452, 7308, 15624, 15624, 7308, 1452, 129},
%e A154915 {257, 3770, 26724, 80640, 108864, 80640, 26724, 3770, 257},
%e A154915 {513, 9546, 94644, 408312, 706608, 706608, 408312, 94644, 9546, 513},
%e A154915 {1025, 23644, 327860, 2068560, 4554560, 5443200, 4554560, 2068560, 327860, 
               23644, 1025}
%t A154915 Clear[t, p, q, n, m, a];
%t A154915 p = 2; q = 1;
%t A154915 t[n_, m_] = (p^(n - m)*q^m + p^m*q^(n - m))*(StirlingS2[n, m] + StirlingS2[n, 
               n - m]);
%t A154915 Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t A154915 Flatten[%]
%Y A154915 Sequence in context: A005589 A052360 A154913 this_sequence A006994 A038627 
               A155835
%Y A154915 Adjacent sequences: A154912 A154913 A154914 this_sequence A154916 A154917 
               A154918
%K A154915 nonn,tabf,uned,tabl
%O A154915 0,1
%A A154915 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 17 2009