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 A210040 Array of coefficients of polynomials v(n,x) jointly generated with A210039; see the Formula section. 3
 1, 2, 1, 3, 4, 4, 10, 1, 5, 20, 6, 6, 35, 21, 1, 7, 56, 56, 8, 8, 84, 126, 36, 1, 9, 120, 252, 120, 10, 10, 165, 462, 330, 55, 1, 11, 220, 792, 792, 220, 12, 12, 286, 1287, 1716, 715, 78, 1, 13, 364, 2002, 3432, 2002, 364, 14, 14, 455, 3003, 6435, 5005, 1365 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Every term is a binomial coefficient. Row sums:  A000225 For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=u(n-1,x)+v(n-1,x)+1, v(n,x)=x*u(n-1,x)+v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. Also: writing T(n,m) for the general term, T(n,1)=n for n>=1; T(n,k)=C(n+1,2k-1) for 1<=k<=floor[(n+2)/2]. EXAMPLE First eight rows: 1 2...1 3...4 4...10...1 5...20...6 6...35...21....1 7...56...56....8 8...84...126...36...1 First five polynomials v(n,x): 1 2 + x 3 + 4x. 4 + 10x + x^2 5 + 20x + 6x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1; v[n_, x_] := x*u[n - 1, 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[%]    (* A210039 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A210040 *) Table[u[n, x] /. x -> 1, {n, 1, z}] (* A000225 *) Table[v[n, x] /. x -> 1, {n, 1, z}] (* A000225 *) CROSSREFS Cf. A210039, A208510. Sequence in context: A033799 A325324 A241745 * A285329 A289023 A085985 Adjacent sequences:  A210037 A210038 A210039 * A210041 A210042 A210043 KEYWORD nonn,tabf AUTHOR Clark Kimberling, Mar 17 2012 STATUS approved

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)