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 A210199 Triangle of coefficients of polynomials u(n,x) jointly generated with A210200; see the Formula section. 3
 1, 3, 6, 2, 11, 7, 2, 19, 19, 9, 2, 32, 44, 30, 11, 2, 53, 94, 83, 43, 13, 2, 87, 190, 207, 137, 58, 15, 2, 142, 370, 480, 387, 208, 75, 17, 2, 231, 701, 1057, 1004, 653, 298, 94, 19, 2, 375, 1301, 2238, 2448, 1865, 1026, 409, 115, 21, 2, 608, 2376, 4596 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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+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 3 6....2 11...7....2 19...19...9...2 First three polynomials u(n,x): 1, 3, 6 + 2x. 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 + 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[%]   (* A210199 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]  (* A210200 *) CROSSREFS Cf. A210200, A208510. Sequence in context: A210189 A257506 A210035 * A268717 A002516 A073807 Adjacent sequences:  A210196 A210197 A210198 * A210200 A210201 A210202 KEYWORD nonn,tabf AUTHOR Clark Kimberling, Mar 18 2012 STATUS approved

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Last modified March 30 19:49 EDT 2020. Contains 333127 sequences. (Running on oeis4.)