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 A210232 Triangle of coefficients of polynomials v(n,x) jointly generated with A210231; see the Formula section. 3
 1, 2, 2, 3, 5, 3, 4, 10, 10, 4, 5, 16, 25, 18, 5, 6, 24, 48, 54, 30, 6, 7, 33, 84, 123, 106, 47, 7, 8, 44, 132, 246, 282, 194, 70, 8, 9, 56, 198, 438, 637, 594, 336, 100, 9, 10, 70, 280, 730, 1272, 1504, 1170, 556, 138, 10, 11, 85, 385, 1140, 2337, 3337, 3301 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First and last terms of row n are n. Alternating row sums: 1,0,1,0,1,0,1,0,1,0,... For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+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...2 3...5....3 4...10...10...4 5...16...25...16...5 First three polynomials v(n,x): 1, 2 + 2x , 3 + 5x + 3x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1; v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%]     (* A210231 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]     (* A210232 *) CROSSREFS Cf. A210231, A208510. Sequence in context: A210565 A125101 A208519 * A047666 A285935 A209568 Adjacent sequences:  A210229 A210230 A210231 * A210233 A210234 A210235 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 20 2012 STATUS approved

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Last modified October 18 05:07 EDT 2019. Contains 328145 sequences. (Running on oeis4.)