%I A156896
%S A156896 1,1,1,1,0,1,1,4,1,4,2,0,1,1,11,11,10,22,3,11,3,0,1,1,26,66,0,
%T A156896 131,78,62,78,6,26,4,0,1,1,57,302,245,547,905,74,901,342,292,
%U A156896 228,10,57,5,0,1,1,120,1191,2296,1191,7128,3572,6648,7140,1216
%V A156896 1,1,1,-1,0,1,1,-4,1,4,-2,0,1,1,-11,11,10,-22,3,11,-3,0,1,1,-26,66,0,
%W A156896 -131,78,62,-78,6,26,-4,0,1,1,-57,302,-245,-547,905,74,-901,342,292,
%X A156896 -228,10,57,-5,0,1,1,-120,1191,-2296,-1191,7128,-3572,-6648,7140,1216
%N A156896 A infinite sum polynomial triangle of coefficients based on the Padovan/ 
               Minimal Pisot: p(x,n)=p[x_, n_] = ((1 + x - x^3)^ (n + 1))*Sum[(k 
               + 1)^n*(-x + x^3)^k, {k, 0, Infinity}].
%C A156896 Row sums are one.
%C A156896 Second column is negative Eulerian numbers.
%F A156896 p(x,n)=p[x_, n_] = ((1 + x - x^3)^ (n + 1))*Sum[(k + 1)^n*(-x + x^3)^k, 
               {k, 0, Infinity}];
%F A156896 t*n,m)=coefficients(p(x,n)).
%e A156896 {1},
%e A156896 {1},
%e A156896 {1, -1, 0, 1},
%e A156896 {1, -4, 1, 4, -2, 0, 1},
%e A156896 {1, -11, 11, 10, -22, 3, 11, -3, 0, 1},
%e A156896 {1, -26, 66, 0, -131, 78, 62, -78, 6, 26, -4, 0, 1},
%e A156896 {1, -57, 302, -245, -547, 905, 74, -901, 342, 292, -228, 10, 57, -5, 
               0, 1},
%e A156896 {1, -120, 1191, -2296, -1191, 7128, -3572, -6648, 7140, 1216, -4749, 
               1200, 1171, -600, 15, 120, -6, 0, 1},
%e A156896 {1, -247, 4293, -15372, 7033, 42564, -57936, -25393, 92232, -27304, -58771, 
               42909, 10679, -21430, 3705, 4258, -1482, 21, 247, -7, 0, 1},
%e A156896 {1, -502, 14608, -87732, 126974, 176468, -595544, 175966, 849493, -790592, 
               -405648, 871798, -135942, -423600, 219064, 70664, -87578, 10542, 
               14552, -3514, 28, 502, -8, 0, 1},
%e A156896 {1, -1013, 47840, -454179, 1214674, 55222, -4738384, 5138354, 5131985, 
               -12313469, 1578360, 12098909, -7765122, -4877406, 6771152, -363962, 
               -2660242, 1004514, 398464, -334754, 28364, 47756, -8104, 36, 1013, 
               -9, 0, 1}
%t A156896 Clear[p, x, n, m];
%t A156896 p[x_, n_] = ((1 + x - x^3)^ (n + 1))*Sum[(k + 1)^n*(-x + x^3)^k, {k, 
               0, Infinity}];
%t A156896 Table[Expand[FullSimplify[ExpandAll[p[x, n]]]], {n, 0, 10}];
%t A156896 Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
%t A156896 Flatten[%]
%Y A156896 Sequence in context: A097936 A050338 A077088 this_sequence A002193 A020807 
               A055190
%Y A156896 Adjacent sequences: A156893 A156894 A156895 this_sequence A156897 A156898 
               A156899
%K A156896 tabl,uned,sign
%O A156896 0,8
%A A156896 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 17 2009