%I A155868
%S A155868 1,1,1,1,1,1,1,6,6,1,1,36,121,36,1,1,240,1750,1750,240,1,1,1800,23290,
%T A155868 50625,23290,1800,1,1,15120,308700,1193640,1193640,308700,15120,1,1,
%U A155868 141120,4207896,25738720,45819361,25738720,4207896,141120,1,1,1451520
%N A155868 A sequence of polynomial coefficients related to the first Stirling numbers: 
               p(x,n)=If[n == 0, 1, 1 + x^n + Sum[(-1)^(n - 2*m)* StirlingS1[n, 
               m]*StirlingS1[n, n - m]*x^m, {m, 0, n}]].
%C A155868 Row sums are:
%C A155868 {1, 2, 3, 14, 195, 3982, 100807, 3034922, 105994835, 4215106730, 188097696347,
               ...}
%F A155868 p(x,n)=If[n == 0, 1, 1 + x^n + Sum[(-1)^(n - 2*m)* StirlingS1[n, m]*StirlingS1[n, 
               n - m]*x^m, {m, 0, n}]]
%F A155868 t(n,m)=coefficients(p(x,n))
%e A155868 {1},
%e A155868 {1, 1},
%e A155868 {1, 1, 1},
%e A155868 {1, 6, 6, 1},
%e A155868 {1, 36, 121, 36, 1},
%e A155868 {1, 240, 1750, 1750, 240, 1},
%e A155868 {1, 1800, 23290, 50625, 23290, 1800, 1},
%e A155868 {1, 15120, 308700, 1193640, 1193640, 308700, 15120, 1},
%e A155868 {1, 141120, 4207896, 25738720, 45819361, 25738720, 4207896, 141120, 1},
%e A155868 {1, 1451520, 59832864, 535810464, 1510458516, 1510458516, 535810464, 
               59832864, 1451520, 1},
%e A155868 {1, 16329600, 893121120, 11082015000, 45789404640, 72535955625, 45789404640, 
               11082015000, 893121120, 16329600, 1}
%t A155868 Clear[p, n, m, x, a];
%t A155868 p[x_, n_] = If[n == 0, 1, 1 + x^n + Sum[(-1)^(n - 2*m)* StirlingS1[n, 
               m]*StirlingS1[n, n - m]*x^m, {m, 0, n}]];
%t A155868 Table[ExpandAll[p[x, n]], {n, 0, 10}];
%t A155868 a = Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];
%t A155868 Flatten[a]
%Y A155868 Sequence in context: A046619 A021606 A046606 this_sequence A065493 A133890 
               A111719
%Y A155868 Adjacent sequences: A155865 A155866 A155867 this_sequence A155869 A155870 
               A155871
%K A155868 nonn,tabl,uned
%O A155868 0,8
%A A155868 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 29 2009