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Search: id:A136452
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| A136452 |
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A129065 with v=x instead of v=1: recursive polynomial coefficient triangle. |
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+0
1
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| 1, 1, 4, 0, -1, 36, 0, -17, 4, 576, 0, -380, 148, -15, 14400, 0, -11804, 5908, -1015, 56, 518400, 0, -496944, 290928, -65120, 6116, -185, 25401600, 0, -27460656, 17936112, -4733696, 577556, -28385, 204, 1625702400, 0, -1935293184, 1371808128, -405733232, 57923264, -3462648, -6152, 6209
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are:
{1, 1, 3, 23, 329, 7545, 253195, 11692735, 710944785, 55043460305,
5286546264275}
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FORMULA
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v=x; p(n, x) = (x + 2*(n - 1)^2 - 2*(v - 1)*(n - 1) - v + 1)*p(n - 1, x) - (n - 1)^2*(n - 1 - v)^2*p(n - 2, x)
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EXAMPLE
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{1},
{1},
{4, 0, -1},
{36, 0, -17,4},
{576, 0, -380, 148, -15},
{14400, 0, -11804, 5908, -1015,56},
{518400, 0, -496944, 290928, -65120, 6116, -185},
{25401600, 0, -27460656, 17936112, -4733696, 577556, -28385, 204},
{1625702400, 0, -1935293184, 1371808128, -405733232, 57923264, -3462648, -6152,6209},
{131681894400, 0, -169764367104, 128290843008, -41266969200, 6529719744, -418217336, -12355080, 3024273, -112400},
{13168189440000, 0, -18161573760000, 14454310602240, -4959685865664, 841974673536, -53197348976, -4408319328, 1000552476, -65230280, 1520271}
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MATHEMATICA
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Clear[p, v, x, n] p[ -1, x] = 0 ; p[0, x] = 1; p[n_, x_] := p[n, x] = (x + 2*(n - 1)^2 - 2*(v - 1)*(n - 1) - v + 1)*p[n - 1, x] - (n - 1)^2*(n - 1 - v)^2*p[n - 2, x]; v = x; a = Join[{{1}}, Table[CoefficientList[p[n, x], x], {n, 1, 10}]]; Flatten[a]
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CROSSREFS
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Cf. A129065.
Adjacent sequences: A136449 A136450 A136451 this_sequence A136453 A136454 A136455
Sequence in context: A059056 A127153 A054375 this_sequence A067565 A010635 A019200
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 19 2008
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