Search: id:A155863
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%I A155863
%S A155863 1,1,1,1,6,1,1,24,24,1,1,60,120,60,1,1,120,360,360,120,1,1,210,840,1260,
%T A155863 840,210,1,1,336,1680,3360,3360,1680,336,1,1,504,3024,7560,10080,7560,
%U A155863 3024,504,1,1,720,5040,15120,25200,25200,15120,5040,720,1,1,990,7920
%N A155863 A sequence of polynomial coefficients related to the third derivative 
               of the Pascal triangle: p(x,n)=x^n+1+x*d^3(x+1)^(n+1)/dx^3=If[n == 
               0, 1, x^n + 1 + x*D[(x + 1)^(n + 1), {x, 3}]].
%C A155863 Row sums are:
%C A155863 {1, 2, 8, 50, 242, 962, 3362, 10754, 32258, 92162, 253442,...}
%F A155863 p(x,n)=x^n+1+x*d^3(x+1)^(n+1)/dx^3
%F A155863 p(x,n)=If[n == 0, 1, x^n + 1 + x*D[(x + 1)^(n + 1), {x, 3}]]
%F A155863 t(n,m)=coefficients(p(x,n))
%e A155863 {1},
%e A155863 {1, 1},
%e A155863 {1, 6, 1},
%e A155863 {1, 24, 24, 1},
%e A155863 {1, 60, 120, 60, 1},
%e A155863 {1, 120, 360, 360, 120, 1},
%e A155863 {1, 210, 840, 1260, 840, 210, 1},
%e A155863 {1, 336, 1680, 3360, 3360, 1680, 336, 1},
%e A155863 {1, 504, 3024, 7560, 10080, 7560, 3024, 504, 1},
%e A155863 {1, 720, 5040, 15120, 25200, 25200, 15120, 5040, 720, 1},
%e A155863 {1, 990, 7920, 27720, 55440, 69300, 55440, 27720, 7920, 990, 1}
%t A155863 Clear[p, n, m, x, a];
%t A155863 p[x_, n_] = If[n == 0, 1, x^n + 1 + x*D[(x + 1)^(n + 1), {x, 3}]];
%t A155863 Table[ExpandAll[p[x, n]], {n, 0, 10}];
%t A155863 a = Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];
%t A155863 Flatten[a]
%Y A155863 Sequence in context: A152969 A060187 A156139 this_sequence A035348 A140945 
               A141688
%Y A155863 Adjacent sequences: A155860 A155861 A155862 this_sequence A155864 A155865 
               A155866
%K A155863 nonn,uned
%O A155863 0,5
%A A155863 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 29 2009

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