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 A146565 A double offset polynomial as a triangle of coefficients: p(x,n)=(x + 1)^n + If[n >= 2, x^2*(x + 1)^(n - 1), x^(n + 1)] + If[n >= 4, x^2*(x + 1)^(n - 3), 0]. 1
 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 4, 3, 1, 1, 4, 8, 8, 4, 1, 1, 5, 12, 16, 12, 5, 1, 1, 6, 17, 28, 28, 17, 6, 1, 1, 7, 23, 45, 56, 45, 23, 7, 1, 1, 8, 30, 68, 101, 101, 68, 30, 8, 1, 1, 9, 38, 98, 169, 202, 169, 98, 38, 9, 1, 1, 10, 47, 136, 267, 371, 371, 267, 136, 47, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Row sums are {1, 2, 3, 6, 12, 26, 52, 104, 208, 416, 832, 1664, ...}, A259098. LINKS FORMULA p(x,n)=(x + 1)^n + If[n >= 2, x^2*(x + 1)^(n - 1), x^(n + 1)] + If[n >= 4, x^2*(x + 1)^(n - 3), 0]; t(n,m)=Coefficients(p(x,n)). EXAMPLE Triangle begins: {1}, {1, 1}, {1, 1, 1}, {1, 2, 2, 1}, {1, 3, 4, 3, 1}, {1, 4, 8, 8, 4, 1}, {1, 5, 12, 16, 12, 5, 1}, {1, 6, 17, 28, 28, 17, 6, 1}, {1, 7, 23, 45, 56, 45, 23, 7, 1}, {1, 8, 30, 68, 101, 101, 68, 30, 8, 1}, {1, 9, 38, 98, 169, 202, 169, 98, 38, 9, 1}, {1, 10, 47, 136, 267, 371, 371, 267, 136, 47, 10, 1}, ... MATHEMATICA p[x_, n_] = (x + 1)^n + If[n >= 2, x^2*(x + 1)^(n - 1), x^(n + 1)] + If[n >= 4, x^2*(x + 1)^(n - 3), 0]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%] CROSSREFS Cf. A072405, A259098. Sequence in context: A047089 A122218 A072405 * A115594 A086623 A248736 Adjacent sequences: A146562 A146563 A146564 * A146566 A146567 A146568 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Nov 01 2008 EXTENSIONS Partially edited by N. J. A. Sloane, Jun 22 2015 STATUS approved

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Last modified February 5 08:15 EST 2023. Contains 360082 sequences. (Running on oeis4.)