%I A154913
%S A154913 4,3,3,5,8,5,9,6,6,9,17,120,176,120,17,33,252,180,180,252,33,65,
%T A154913 4590,7180,7200,7180,4590,65,129,46134,57204,21336,21336,57204,
%U A154913 46134,129,257,658840,910520,603680,433216,603680,910520,658840,257
%V A154913 4,3,3,5,-8,5,9,-6,-6,9,17,-120,176,-120,17,33,252,-180,-180,252,33,65,
%W A154913 -4590,7180,-7200,7180,-4590,65,129,46134,-57204,21336,21336,-57204,
%X A154913 46134,129,257,-658840,910520,-603680,433216,-603680,910520,-658840,257
%N A154913 A triangular sequence: p = 2; q = 1; t(n,m) = (p^(n - m)*q^m + p^m*q^( 
               n - m))*(StirlingS1[n, m] + StirlingS1[n, n - m]).
%C A154913 Row sums are:
%C A154913 {4, 6, 2, 6, -30, 210, -1890, 20790, -270270, 4054050, -68918850,..}.
%C A154913 Fractal Plot:
%C A154913 a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 243}];
%C A154913 b = Table[If[m <= n, 3 - Mod[a[[n]][[m]], 3], 0], {m, 1, Length[a]}, 
               {n, 1, Length[a]}];
%C A154913 ListDensityPlot[b, Mesh -> False, Frame -> False, AspectRatio -> Automatic, 
               ColorFunction -> (Hue[2# ] &)]
%F A154913 p = 2; q = 1;
%F A154913 t(n,m) = (p^(n - m)*q^m + p^m*q^(n - m))*(StirlingS1[n, m] + StirlingS1[n, 
               n - m]).
%e A154913 {4},
%e A154913 {3, 3},
%e A154913 {5, -8, 5},
%e A154913 {9, -6, -6, 9},
%e A154913 {17, -120, 176, -120, 17},
%e A154913 {33, 252, -180, -180, 252, 33},
%e A154913 {65, -4590, 7180, -7200, 7180, -4590, 65},
%e A154913 {129, 46134, -57204, 21336, 21336, -57204, 46134, 129},
%e A154913 {257, -658840, 910520, -603680, 433216, -603680, 910520, -658840, 257},
%e A154913 {513, 10393272, -14393016, 8178336, -2152080, -2152080, 8178336, -14393016, 
               10393272, 513},
%e A154913 {1025, -186543450, 267135960, -160772400, 62956240, -34473600, 62956240, 
               -160772400, 267135960, -186543450, 1025}
%t A154913 Clear[t, p, q, n, m, a];
%t A154913 p = 2; q = 1;
%t A154913 t[n_, m_] = (p^(n - m)*q^m + p^m*q^(n - m))*(StirlingS1[n, m] + StirlingS1[n, 
               n - m]);
%t A154913 Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t A154913 Flatten[%]
%Y A154913 Sequence in context: A063571 A005589 A052360 this_sequence A154915 A006994 
               A038627
%Y A154913 Adjacent sequences: A154910 A154911 A154912 this_sequence A154914 A154915 
               A154916
%K A154913 uned,tabl,sign
%O A154913 0,1
%A A154913 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 17 2009