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 A144395 A designed polynomial set that gives a {1,6,1} quadratic and gives a symmetrical triangle of coefficients: p(x,n)=If[n == 2, 1, ((x + 1)^n -If[n == 0, 1, x^n + (n - 1)*x^(n - 1) + (n - 1)*x + 1])/x],. 0
 1, 1, 1, 1, 6, 1, 1, 10, 10, 1, 1, 15, 20, 15, 1, 1, 21, 35, 35, 21, 1, 1, 28, 56, 70, 56, 28, 1, 1, 36, 84, 126, 126, 84, 36, 1, 1, 45, 120, 210, 252, 210, 120, 45, 1, 1, 55, 165, 330, 462, 462, 330, 165, 55, 1, 1, 66, 220, 495, 792, 924, 792, 495, 220, 66, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums are:{1, 2, 8, 22, 52, 114, 240, 494, 1004, 2026, 4072}. LINKS FORMULA p(x,n)=If[n == 2, 1, ((x + 1)^n -If[n == 0, 1, x^n + (n - 1)*x^(n - 1) + (n - 1)*x + 1])/x]; t(n,m)=coefficients(p(x,n)). EXAMPLE {1}, {1, 1}, {1, 6, 1}, {1, 10, 10, 1}, {1, 15, 20, 15, 1}, {1, 21, 35, 35, 21, 1}, {1, 28, 56, 70, 56, 28, 1}, {1, 36, 84, 126, 126, 84, 36, 1}, {1, 45, 120, 210, 252, 210, 120, 45, 1}, {1, 55, 165, 330, 462, 462, 330, 165, 55, 1}, {1, 66, 220, 495, 792, 924, 792, 495, 220, 66, 1} MATHEMATICA Clear[p, x, n] p[x_, n_] = If[ n == 2, 1, ((x + 1)^n - If[n == 0, 1, x^n + (n - 1)*x^(n - 1) + (n - 1)*x + 1])/x]; Table[ExpandAll[p[x, n]], {n, 2, 12}]; Table[CoefficientList[p[x, n], x], {n, 2, 12}]; Flatten[%] CROSSREFS Sequence in context: A174377 A176151 A204001 * A046621 A046617 A131063 Adjacent sequences:  A144392 A144393 A144394 * A144396 A144397 A144398 KEYWORD nonn,uned AUTHOR Roger L. Bagula and Gary W. Adamson, Oct 02 2008 STATUS approved

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Last modified September 20 00:48 EDT 2021. Contains 347577 sequences. (Running on oeis4.)