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 A207537 Triangle of coefficients of polynomials u(n,x) jointly generated with A207538; see Formula section. 4
 1, 2, 1, 4, 3, 8, 8, 1, 16, 20, 5, 32, 48, 18, 1, 64, 112, 56, 7, 128, 256, 160, 32, 1, 256, 576, 432, 120, 9, 512, 1280, 1120, 400, 50, 1, 1024, 2816, 2816, 1232, 220, 11, 2048, 6144, 6912, 3584, 840, 72, 1, 4096, 13312, 16640, 9984, 2912, 364, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Another version in A201701. - Philippe Deléham, Mar 03 2012. Subtriangle of the triangle given by (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 03 2012 Columns : A011782, A001792, A001793, A001794, A006974, A006975, A006976. - Philippe Deléham, Mar 03 2012 Diagonal sums : A052980. - Philippe Deléham, Mar 03 2012 LINKS FORMULA u(n,x)=u(n-1,x)+(x+1)*v(n-1,x), v(n,x)=u(n-1,x)+v(n-1,x), where u(1,x)=1, v(1,x)=1.  Also, A207537=|A028297|. T(n,k) = 2*T(n-1,k) + T(n-2,k-1). - Philippe Deléham, Mar 03 2012 G.f.: -(1+x*y)*x*y/(-1+2*x+x^2*y). - R. J. Mathar, Aug 11 2015 EXAMPLE First seven rows: 1 2...1 4...3 8...8...1 16..20..5 32..48..18..1 64..112.56..7 Triangle A201701 begins : 1 1, 0 2, 1, 0 4, 3, 0, 0 8, 8, 1, 0, 0 16, 20, 5, 0, 0, 0 32, 48, 18, 1, 0, 0, 0 64, 112, 56, 7, 0, 0, 0, 0 ... - Philippe Deléham, Mar 03 2012 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] v[n_, x_] := u[n - 1, x] + v[n - 1, x] Table[Factor[u[n, x]], {n, 1, z}] Table[Factor[v[n, x]], {n, 1, z}] cu = Table[CoefficientList[u[n, x], x], {n, 1, z}]; TableForm[cu] Flatten[%]  (* A207537, |A028297| *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]  (* A207538, |A133156| *) CROSSREFS Cf. A028297, A207538, A133156. Sequence in context: A005291 A106624 A028297 * A114438 A238757 A306888 Adjacent sequences:  A207534 A207535 A207536 * A207538 A207539 A207540 KEYWORD nonn,tabf AUTHOR Clark Kimberling, Feb 18 2012 STATUS approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)