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 A210219 Triangle of coefficients of polynomials u(n,x) jointly generated with A210220; see the Formula section. 3
 1, 2, 1, 3, 4, 1, 4, 9, 7, 1, 5, 16, 22, 11, 1, 6, 25, 50, 46, 16, 1, 7, 36, 95, 130, 86, 22, 1, 8, 49, 161, 295, 296, 148, 29, 1, 9, 64, 252, 581, 791, 610, 239, 37, 1, 10, 81, 372, 1036, 1792, 1897, 1163, 367, 46, 1, 11, 100, 525, 1716, 3612, 4900, 4166 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First two terms in row n: n,(n-1)^2; last term: 1 Period of alternating row sums: (1,1,0) For a discussion and guide to related arrays, see A208510. Apparently this is A071920 without the marginal zeros, read downwards antidiagonals, or T(n,k) = A071922(n,k). - R. J. Mathar, May 17 2014 LINKS FORMULA u(n,x)=x*u(n-1,x)+v(n-1,x)+1, v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 2...1 3...4....1 4...9....7....1 5...16...22...11...1 First three polynomials u(n,x): 1, 2 + x, 3 + 4x + x^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*u[n - 1, x] + (x + 1)*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[%] (* A210219 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%] (* A210220 *) CROSSREFS Cf. A210220, A208510, A001906 (row sums). Sequence in context: A103283 A104698 A067066 * A125103 A171275 A335312 Adjacent sequences: A210216 A210217 A210218 * A210220 A210221 A210222 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 19 2012 STATUS approved

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Last modified December 2 17:17 EST 2022. Contains 358510 sequences. (Running on oeis4.)