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Search: id:A154986
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| A154986 |
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Polynomial recursion: p(x, n) = (x + 1)*p(x, n - 1) + (n^2 - n)*x*p(x, n - 2). |
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+0
1
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| 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; listen)
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OFFSET
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0,5
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COMMENT
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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.
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FORMULA
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p(x, n) = (x + 1)*p(x, n - 1) + (n^2 - n)*x*p(x, n - 2).;
t(n,m)=coefficients(p(x,n))
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EXAMPLE
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{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}
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MATHEMATICA
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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[%]
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CROSSREFS
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A008292,A000142
Sequence in context: A154096 A146898 A152970 this_sequence A154983 A156534 A008292
Adjacent sequences: A154983 A154984 A154985 this_sequence A154987 A154988 A154989
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 18 2009
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