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A154986 Polynomial recursion: p(x, n) = (x + 1)*p(x, n - 1) + (n^2 - n)*x*p(x, n - 2). 0

%I

%S 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 1079,76,1,1,119,3045,16995,16995,3045,119,1,1,176,7420,80464,186758,

%U 80464,7420,176,1,1,249,16164,307124,1490862,1490862,307124,16164,249,1

%N Polynomial recursion: p(x, n) = (x + 1)*p(x, n - 1) + (n^2 - n)*x*p(x, n - 2).

%C Row sums are:A000142;

%C {1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800,...}.

%C The sequence is row sum dual to the Eulerian numbers A008292.

%F p(x, n) = (x + 1)*p(x, n - 1) + (n^2 - n)*x*p(x, n - 2).;

%F t(n,m)=coefficients(p(x,n))

%e {1},

%e {1, 1},

%e {1, 4, 1},

%e {1, 11, 11, 1},

%e {1, 24, 70, 24, 1},

%e {1, 45, 314, 314, 45, 1},

%e {1, 76, 1079, 2728, 1079, 76, 1},

%e {1, 119, 3045, 16995, 16995, 3045, 119, 1},

%e {1, 176, 7420, 80464, 186758, 80464, 7420, 176, 1},

%e {1, 249, 16164, 307124, 1490862, 1490862, 307124, 16164, 249, 1},

%e {1, 340, 32253, 991088, 9039746, 19789944, 9039746, 991088, 32253, 340, 1}

%t Clear[p, n, m, x]; m = 1; p[x, 0] = 1; p[x, 1] = x + 1;

%t p[x_, n_] := p[x, n] = (x + 1)*p[x, n - 1] + (n^2 - n)*x*p[x, n - 2];

%t Table[ExpandAll[p[x, n]], {n, 0, 10}];

%t Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];

%t Flatten[%]

%Y A008292,A000142

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Jan 18 2009

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Last modified September 19 18:21 EDT 2020. Contains 337181 sequences. (Running on oeis4.)