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 A208508 Triangle of coefficients of polynomials u(n,x) jointly generated with A208509; see the Formula section. 4
 1, 1, 1, 1, 4, 1, 9, 1, 1, 16, 6, 1, 25, 20, 1, 1, 36, 50, 8, 1, 49, 105, 35, 1, 1, 64, 196, 112, 10, 1, 81, 336, 294, 54, 1, 1, 100, 540, 672, 210, 12, 1, 121, 825, 1386, 660, 77, 1, 1, 144, 1210, 2640, 1782, 352, 14, 1, 169, 1716, 4719, 4290, 1287, 104, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS col 1: A000012 col 2: A000290 (squares) col 3: A002415 col 4: A040977 col 5: A054334 row sums, u(n,1): A083329 LINKS Table of n, a(n) for n=1..64. FORMULA u(n,x)=u(n-1,x)+x*v(n-1,x), v(n,x)=u(n-1,x)+v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 1...1 1...4 1...9....1 1...16...6 First five polynomials u(n,x): 1 1 + x 1 + 4x 1 + 9x + x^2 1 + 16x + 6x^2 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + x*v[n - 1, x]; v[n_, 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[%] (* A208508 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%] (* A208509 *) CROSSREFS Cf. A208509. Sequence in context: A143469 A360610 A331147 * A123726 A323600 A336851 Adjacent sequences: A208505 A208506 A208507 * A208509 A208510 A208511 KEYWORD nonn,tabf AUTHOR Clark Kimberling, Feb 27 2012 STATUS approved

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Last modified February 23 06:36 EST 2024. Contains 370267 sequences. (Running on oeis4.)