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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
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, 1079, 76, 1, 1, 119, 3045, 16995, 16995, 3045, 119, 1, 1, 176, 7420, 80464, 186758, 80464, 7420, 176, 1, 1, 249, 16164, 307124, 1490862, 1490862, 307124, 16164, 249, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:A000142;

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

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

LINKS

Table of n, a(n) for n=0..54.

FORMULA

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

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

EXAMPLE

{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, 1079, 76, 1},

{1, 119, 3045, 16995, 16995, 3045, 119, 1},

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

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

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

MATHEMATICA

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

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

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

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

Flatten[%]

CROSSREFS

A008292,A000142

Sequence in context: A154096 A146898 A152970 * A154983 A156534 A168287

Adjacent sequences:  A154983 A154984 A154985 * A154987 A154988 A154989

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 18 2009

STATUS

approved

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Last modified October 22 18:55 EDT 2018. Contains 316500 sequences. (Running on oeis4.)