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Search: id:A147564
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| A147564 |
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A set of Pascal triangle based polynomials: p(x,n)=If[n >= 0, -2 + 2*(1 + x)^n, 0] + (1 + x)^(1 + n) + If[n >1, 2*x*D[(1 + x)^n, {x, 1}], 0]. |
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+0
1
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| 1, 1, 1, 1, 4, 1, 1, 11, 9, 1, 1, 16, 24, 12, 1, 1, 21, 46, 42, 15, 1, 1, 26, 75, 100, 65, 18, 1, 1, 31, 111, 195, 185, 93, 21, 1, 1, 36, 154, 336, 420, 308, 126, 24, 1, 1, 41, 204, 532, 826, 798, 476, 164, 27, 1, 1, 46, 261, 792, 1470, 1764, 1386, 696, 207, 30, 1, 1, 51, 325
(list; graph; listen)
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OFFSET
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-1,5
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COMMENT
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The row sums are:{1, 2, 6, 22, 54, 126, 286, 638, 1406, 3070, 6654, 14334,...}
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FORMULA
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p(x,n)=If[n >= 0, -2 + 2*(1 + x)^n, 0] + (1 + x)^(1 + n) + If[n >1, 2*x*D[(1 + x)^n, {x, 1}], 0]; t(n,m)=coefficients(t(n,m)).
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EXAMPLE
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{1}, {1, 1}, {1, 4, 1}, {1, 11, 9, 1}, {1, 16, 24, 12, 1}, {1, 21, 46, 42, 15, 1}, {1, 26, 75, 100, 65, 18, 1}, {1, 31, 111, 195, 185, 93, 21, 1}, {1, 36, 154, 336, 420, 308, 126, 24, 1}, {1, 41, 204, 532, 826, 798, 476, 164, 27, 1}, {1, 46, 261, 792, 1470, 1764, 1386, 696, 207, 30, 1}, {1, 51, 325, 1125, 2430, 3486, 3402, 2250, 975, 255, 33, 1}
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MATHEMATICA
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Clear[t, p, x, n]; p[x_, n_] = If[n >= 0, -2 + 2*(1 + x)^n, 0] + (1 + x)^(1 + n) + If[n > 1, 2*x*D[(1 + x)^n, {x, 1}], 0]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, -1, 10}]; Flatten[%]
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CROSSREFS
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Adjacent sequences: A147561 A147562 A147563 this_sequence A147565 A147566 A147567
Sequence in context: A164366 A121692 A145271 this_sequence A090981 A087903 A112500
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 07 2008
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