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Search: id:A154982
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| A154982 |
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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). |
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+0
1
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| 1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 18, 50, 18, 1, 1, 35, 212, 212, 35, 1, 1, 68, 823, 2024, 823, 68, 1, 1, 133, 3131, 16415, 16415, 3131, 133, 1, 1, 262, 11968, 124890, 291902, 124890, 11968, 262, 1, 1, 519, 46278, 938394, 4619032, 4619032, 938394, 46278, 519
(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, 20, 88, 496, 3808, 39360, 566144, 11208448, 312282624,...}.
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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);
t(n,m)=coefficients(p(x,n))
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EXAMPLE
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{1},
{1, 1},
{1, 4, 1},
{1, 9, 9, 1},
{1, 18, 50, 18, 1},
{1, 35, 212, 212, 35, 1},
{1, 68, 823, 2024, 823, 68, 1},
{1, 133, 3131, 16415, 16415, 3131, 133, 1},
{1, 262, 11968, 124890, 291902, 124890, 11968, 262, 1},
{1, 519, 46278, 938394, 4619032, 4619032, 938394, 46278, 519, 1},
{1, 1032, 180941, 7112288, 69501106, 158691888, 69501106, 7112288, 180941, 1032, 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_] := 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
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Sequence in context: A124216 A008459 A157192 this_sequence A146767 A146955 A155451
Adjacent sequences: A154979 A154980 A154981 this_sequence A154983 A154984 A154985
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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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