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 A210753 Triangle of coefficients of polynomials u(n,x) jointly generated with A210754; see the Formula section. 3
 1, 2, 2, 3, 7, 4, 4, 16, 20, 8, 5, 30, 61, 52, 16, 6, 50, 146, 198, 128, 32, 7, 77, 301, 575, 584, 304, 64, 8, 112, 560, 1408, 1992, 1616, 704, 128, 9, 156, 966, 3060, 5641, 6328, 4272, 1600, 256, 10, 210, 1572, 6084, 14002, 20330, 18880, 10912, 3584 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row n starts with n and ends with 2^(n-1). Row sums: A007070 Alternating row sums: 1,0,0,0,0,0,0,0,0,.... For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1, v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 2...2 3...7....4 4...16...20...8 5...30...61...52...16 First three polynomials u(n,x): 1, 2 + 2x, 3 + 7x + 4x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1; v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1; Table[Expand[u[n, x]], {n, 1, z/2}] Table[Expand[v[n, x]], {n, 1, z/2}] cu = Table[CoefficientList[u[n, x], x], {n, 1, z}]; TableForm[cu] Flatten[%]    (* A210753 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A210754 *) Table[u[n, x] /. x -> 1, {n, 1, z}] (* A007070 *) Table[v[n, x] /. x -> 1, {n, 1, z}] (* A035344 *) CROSSREFS Cf. A210754, A208510. Sequence in context: A222871 A222779 A222894 * A208762 A209746 A267822 Adjacent sequences:  A210750 A210751 A210752 * A210754 A210755 A210756 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 25 2012 STATUS approved

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Last modified October 18 00:03 EDT 2019. Contains 328135 sequences. (Running on oeis4.)