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A154980
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Polynomial recursion:m=1; 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, 6, 1, 1, 15, 15, 1, 1, 32, 126, 32, 1, 1, 65, 638, 638, 65, 1, 1, 130, 2751, 9340, 2751, 130, 1, 1, 259, 11201, 93755, 93755, 11201, 259, 1, 1, 516, 44740, 809212, 2578550, 809212, 44740, 516, 1, 1, 1029, 177864, 6588864, 51390322, 51390322
(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, 8, 32, 192, 1408, 15104, 210432, 4287488, 116316160, 4623020032,...}.
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FORMULA
| m=1; 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, 6, 1},
{1, 15, 15, 1},
{1, 32, 126, 32, 1},
{1, 65, 638, 638, 65, 1},
{1, 130, 2751, 9340, 2751, 130, 1},
{1, 259, 11201, 93755, 93755, 11201, 259, 1},
{1, 516, 44740, 809212, 2578550, 809212, 44740, 516, 1},
{1, 1029, 177864, 6588864, 51390322, 51390322, 6588864, 177864, 1029, 1},
{1, 2054, 707277, 52580488, 886612274, 2743215844, 886612274, 52580488, 707277, 2054, 1}
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MATHEMATICA
| Clear[p, n, m, x]; m = 1; 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: A152238 A086645 A168291 * A166344 A146766 A176152
Adjacent sequences: A154977 A154978 A154979 * A154981 A154982 A154983
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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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