Search: id:A154986
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%I A154986
%S A154986 1,1,1,1,4,1,1,11,11,1,1,24,70,24,1,1,45,314,314,45,1,1,76,1079,2728,
%T A154986 1079,76,1,1,119,3045,16995,16995,3045,119,1,1,176,7420,80464,186758,
%U A154986 80464,7420,176,1,1,249,16164,307124,1490862,1490862,307124,16164,249,
               1
%N A154986 Polynomial recursion: p(x, n) = (x + 1)*p(x, n - 1) + (n^2 - n)*x*p(x, 
               n - 2).
%C A154986 Row sums are:A000142;
%C A154986 {1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800,...}.
%C A154986 The sequence is row sum dual to the Eulerian numbers A008292.
%F A154986 p(x, n) = (x + 1)*p(x, n - 1) + (n^2 - n)*x*p(x, n - 2).;
%F A154986 t(n,m)=coefficients(p(x,n))
%e A154986 {1},
%e A154986 {1, 1},
%e A154986 {1, 4, 1},
%e A154986 {1, 11, 11, 1},
%e A154986 {1, 24, 70, 24, 1},
%e A154986 {1, 45, 314, 314, 45, 1},
%e A154986 {1, 76, 1079, 2728, 1079, 76, 1},
%e A154986 {1, 119, 3045, 16995, 16995, 3045, 119, 1},
%e A154986 {1, 176, 7420, 80464, 186758, 80464, 7420, 176, 1},
%e A154986 {1, 249, 16164, 307124, 1490862, 1490862, 307124, 16164, 249, 1},
%e A154986 {1, 340, 32253, 991088, 9039746, 19789944, 9039746, 991088, 32253, 340, 
               1}
%t A154986 Clear[p, n, m, x]; m = 1; p[x, 0] = 1; p[x, 1] = x + 1;
%t A154986 p[x_, n_] := p[x, n] = (x + 1)*p[x, n - 1] + (n^2 - n)*x*p[x, n - 2];
%t A154986 Table[ExpandAll[p[x, n]], {n, 0, 10}];
%t A154986 Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];
%t A154986 Flatten[%]
%Y A154986 A008292,A000142
%Y A154986 Sequence in context: A154096 A146898 A152970 this_sequence A154983 A156534 
               A008292
%Y A154986 Adjacent sequences: A154983 A154984 A154985 this_sequence A154987 A154988 
               A154989
%K A154986 nonn,tabl,uned
%O A154986 0,5
%A A154986 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 18 2009

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