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 A147564 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]. 0
 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; refs; listen; history; text; internal format)
 OFFSET -1,5 COMMENTS The row sums are:{1, 2, 6, 22, 54, 126, 286, 638, 1406, 3070, 6654, 14334,...} LINKS FORMULA 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)). EXAMPLE {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} MATHEMATICA 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[%] CROSSREFS Sequence in context: A145271 A232774 A203860 * A090981 A087903 A112500 Adjacent sequences:  A147561 A147562 A147563 * A147565 A147566 A147567 KEYWORD nonn AUTHOR Roger L. Bagula, Nov 07 2008 STATUS approved

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