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 A209998 Triangle of coefficients of polynomials v(n,x) jointly generated with A209996; see the Formula section. 3
 1, 2, 3, 2, 8, 9, 2, 10, 30, 27, 2, 10, 46, 108, 81, 2, 10, 50, 198, 378, 243, 2, 10, 50, 242, 810, 1296, 729, 2, 10, 50, 250, 1122, 3186, 4374, 2187, 2, 10, 50, 250, 1234, 4986, 12150, 14580, 6561, 2, 10, 50, 250, 1250, 5946, 21330, 45198, 48114, 1968 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row n starts 2, 2*5, 2*5^2,... ; ends with 3^(n-1). Conjecture: penultimate term in row n is A199923(n). Alternating row sums: A077925 For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1, v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 2...3 2...8....9 2...10...30...27 2...10...46...108...81 First three polynomials v(n,x): 1, 2 + 3x , 2 + 8x + 9x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1; v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*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[%]    (* A209996 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A209998 *) CROSSREFS Cf. A209996, A208510. Sequence in context: A134347 A057761 A321477 * A163204 A299619 A215269 Adjacent sequences:  A209995 A209996 A209997 * A209999 A210000 A210001 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 23 2012 STATUS approved

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Last modified October 20 02:08 EDT 2019. Contains 328244 sequences. (Running on oeis4.)