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 A210039 Array of coefficients of polynomials u(n,x) jointly generated with A210040; see the Formula section. 3
 1, 3, 6, 1, 10, 5, 15, 15, 1, 21, 35, 7, 28, 70, 28, 1, 36, 126, 84, 9, 45, 210, 210, 45, 1, 55, 330, 462, 165, 11, 66, 495, 924, 495, 66, 1, 78, 715, 1716, 1287, 286, 13, 91, 1001, 3003, 3003, 1001, 91, 1, 105, 1365, 5005, 6435, 3003, 455, 15, 120, 1820 (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 the general term as T(n,m), T(n,k)=C(n,2k) for 1<=k<=floor[(n+1)/2], for n>=1. EXAMPLE First eight rows: 1 3 6....1 10...5 15...15....1 21...35....7 28...70....28...1 36...126...84...9 First five polynomials u(n,x): 1 3 6 + x 10 + 5x 21 + 35x + 7x^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. A034839, A210040, A208510. Sequence in context: A110119 A322310 A152202 * A026250 A210033 A209144 Adjacent sequences:  A210036 A210037 A210038 * A210040 A210041 A210042 KEYWORD nonn,tabf AUTHOR Clark Kimberling, Mar 17 2012 STATUS approved

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Last modified October 17 19:18 EDT 2019. Contains 328127 sequences. (Running on oeis4.)