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 A144398 Coefficients of a symmetrical polynomial set:( Pascal's triangle with central zeros) p(x,n)=If[n <= 4, Sum[Binomial[n, i]*x^i, {i, 0, n}], x^n + n*x^(n - 1) + Binomial[n, 2]*x^(n - 2) + n*x + Binomial[n, 2]*x^2 + 1]. 0
 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 0, 15, 6, 1, 1, 7, 21, 0, 0, 21, 7, 1, 1, 8, 28, 0, 0, 0, 28, 8, 1, 1, 9, 36, 0, 0, 0, 0, 36, 9, 1, 1, 10, 45, 0, 0, 0, 0, 0, 45, 10, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums are: (related to A014206) {1, 2, 4, 8, 16, 32, 44, 58, 74, 92, 112} LINKS FORMULA p(x,n)=If[n <= 4, Sum[Binomial[n, i]*x^i, {i, 0, n}], x^n + n*x^(n - 1) + Binomial[n, 2]*x^(n - 2) + n*x + Binomial[n, 2]*x^2 + 1]; t(n,m)=coefficients(p(x,n)). EXAMPLE {1}, {1, 1}, {1, 2, 1}, {1, 3, 3, 1}, {1, 4, 6, 4, 1}, {1, 5, 10, 10, 5, 1}, {1, 6, 15, 0, 15, 6, 1}, {1, 7, 21, 0, 0, 21, 7, 1}, {1, 8, 28, 0, 0, 0, 28, 8, 1}, {1, 9, 36, 0, 0, 0, 0, 36, 9, 1}, {1, 10, 45, 0, 0, 0, 0, 0, 45, 10, 1} MATHEMATICA Clear[p, n]; p[x_, n_] = If[n <= 4, Sum[Binomial[n, i]*x^i, {i, 0, n}], x^n + n*x^(n - 1) + Binomial[n, 2]*x^(n - 2) + n*x + Binomial[n, 2]*x^2 + 1]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A095145 A095144 A339359 * A034932 A180183 A273914 Adjacent sequences:  A144395 A144396 A144397 * A144399 A144400 A144401 KEYWORD nonn,uned AUTHOR Roger L. Bagula and Gary W. Adamson, Oct 03 2008 STATUS approved

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Last modified September 17 01:53 EDT 2021. Contains 347478 sequences. (Running on oeis4.)