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A154979
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Polynomial recursion:m=2; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2).
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0
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1, 1, 1, 1, 10, 1, 1, 27, 27, 1, 1, 60, 374, 60, 1, 1, 125, 2162, 2162, 125, 1, 1, 254, 9967, 52196, 9967, 254, 1, 1, 511, 42221, 615635, 615635, 42221, 511, 1, 1, 1024, 172780, 5760960, 27955622, 5760960, 172780, 1024, 1, 1, 2049, 697068, 49168044
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are:
{1, 2, 12, 56, 496, 4576, 72640, 1316736, 39825152, 1427987968, 84417887232,...}.
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FORMULA
| m=2; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2);
t(n,m)=coefficients(p(x,n))
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EXAMPLE
| {1},
{1, 1},
{1, 10, 1},
{1, 27, 27, 1},
{1, 60, 374, 60, 1}, {1, 125, 2162, 2162, 125, 1}, {1, 254, 9967, 52196, 9967, 254, 1},
{1, 511, 42221, 615635, 615635, 42221, 511, 1},
{1, 1024, 172780, 5760960, 27955622, 5760960, 172780, 1024, 1},
{1, 2049, 697068, 49168044, 664126822, 664126822, 49168044, 697068, 2049, 1},
{1, 4098, 2796269, 403718552, 12511740946, 58581367500, 12511740946, 403718552, 2796269, 4098, 1}
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MATHEMATICA
| Clear[p, n, m, x]; m = 2; p[x, 0] = 1; p[x, 1] = x + 1;
p[x_, n_] := p[x, n] = (x + 1)*p[x, n - 1] + 2^(m + n - 1)*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
| Sequence in context: A166341 A113280 A159041 * A146765 A190152 A154984
Adjacent sequences: A154976 A154977 A154978 * A154980 A154981 A154982
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KEYWORD
| nonn,tabl,uned,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 18 2009
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