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A154984
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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)+If[n >= 3, 2^(n - 2)*x*p(x, n - 2), 0].
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1, 1, 1, 1, 10, 1, 1, 29, 29, 1, 1, 66, 418, 66, 1, 1, 139, 2572, 2572, 139, 1, 1, 284, 12215, 65336, 12215, 284, 1, 1, 573, 52531, 818287, 818287, 52531, 573, 1, 1, 1150, 216688, 7906658, 39270110, 7906658, 216688, 1150, 1, 1, 2303, 877934, 68639058
(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, 60, 552, 5424, 90336, 1742784, 55519104, 2118725376, 132153466368,...}.
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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)
+If[n >= 3, 2^(n - 2)*x*p(x, n - 2), 0];
t(n,m)=coefficients(p(x,n))
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EXAMPLE
| {1},
{1, 1},
{1, 10, 1},
{1, 29, 29, 1},
{1, 66, 418, 66, 1},
{1, 139, 2572, 2572, 139, 1},
{1, 284, 12215, 65336, 12215, 284, 1},
{1, 573, 52531, 818287, 818287, 52531, 573, 1},
{1, 1150, 216688, 7906658, 39270110, 7906658, 216688, 1150, 1},
{1, 2303, 877934, 68639058, 989843392, 989843392, 68639058, 877934, 2303, 1},
{1, 4608, 3529837, 568766144, 19275422482, 92458020224, 19275422482, 568766144, 3529837, 4608, 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] = (x + 1)*p[ x, n - 1] + 2^(m + n - 1)*x*p[x, n - 2]
+ If[n >= 3, 2^(n - 2)*x*p[x, n - 2], 0];
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: A154979 A146765 A190152 * A173047 A173045 A176491
Adjacent sequences: A154981 A154982 A154983 * A154985 A154986 A154987
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 18 2009
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