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Search: id:A154983
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| A154983 |
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Polynomial recursion:m=0; 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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+0
1
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| 1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 24, 70, 24, 1, 1, 49, 358, 358, 49, 1, 1, 98, 1559, 4076, 1559, 98, 1, 1, 195, 6361, 40003, 40003, 6361, 195, 1, 1, 388, 25372, 345692, 862598, 345692, 25372, 388, 1, 1, 773, 100640, 2813688, 16569442, 16569442, 2813688
(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:
{1, 2, 6, 24, 120, 816, 7392, 93120, 1605504, 38969088, 1310965248,...}.
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FORMULA
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m=0; 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
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{1},
{1, 1},
{1, 4, 1},
{1, 11, 11, 1},
{1, 24, 70, 24, 1},
{1, 49, 358, 358, 49, 1},
{1, 98, 1559, 4076, 1559, 98, 1},
{1, 195, 6361, 40003, 40003, 6361, 195, 1},
{1, 388, 25372, 345692, 862598, 345692, 25372, 388, 1},
{1, 773, 100640, 2813688, 16569442, 16569442, 2813688, 100640, 773, 1},
{1, 1542, 399397, 22400024, 284874586, 695614148, 284874586, 22400024, 399397, 1542, 1}
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MATHEMATICA
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Clear[p, n, m, x]; m = 0; 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
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Sequence in context: A146898 A152970 A154986 this_sequence A156534 A008292 A157221
Adjacent sequences: A154980 A154981 A154982 this_sequence A154984 A154985 A154986
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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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