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%I #2 Mar 30 2012 17:34:40
%S 1,2,2,4,9,4,8,64,64,8,16,625,2401,625,16,32,7776,161051,161051,7776,
%T 32,64,117649,16777216,85766121,16777216,117649,64,128,2097152,
%U 2494357888,78364164096,78364164096,2494357888,2097152,128,256,43046721
%N A polynomial coefficient sequence:p(x,n,m)=(1 + Binomial[n, m]*x)^n
%C Row sums are:
%C {1, 4, 17, 144, 3683, 337718, 119555979, 161721238528, 869612424389639,
%C 17653003315264793202, 1425670580988729857215055,...}.
%F p(x,n,m)=(1 + Binomial[n, m]*x)^n
%e {1},
%e {2, 2},
%e {4, 9, 4},
%e {8, 64, 64, 8},
%e {16, 625, 2401, 625, 16},
%e {32, 7776, 161051, 161051, 7776, 32},
%e {64, 117649, 16777216, 85766121, 16777216, 117649, 64},
%e {128, 2097152, 2494357888, 78364164096, 78364164096, 2494357888, 2097152, 128},
%e {256, 43046721, 500246412961, 111429157112001, 645753531245761, 111429157112001, 500246412961, 43046721, 256},
%e {512, 1000000000, 129961739795077, 231616946283203125, 8594754748609397887, 8594754748609397887, 231616946283203125, 129961739795077, 1000000000, 512},
%e {1024, 25937424601, 42420747482776576, 672749994932560009201, 174913992535407978606601, 1074497011086501939579049, 174913992535407978606601, 672749994932560009201, 42420747482776576, 25937424601, 1024}
%t Clear[p, n, m];
%t p[x_, n_, m_] := (1 + Binomial[n, m]*x)^n;
%t Table[Table[ Apply[Plus, CoefficientList[p[x, n, m], x]], {m, 0, n}], {n, 0, 10}];
%t Flatten[%]
%K nonn,tabl,uned
%O 0,2
%A _Roger L. Bagula_, Apr 10 2010
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