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 A210754 Triangle of coefficients of polynomials v(n,x) jointly generated with A210753; see the Formula section. 4
 1, 3, 2, 6, 9, 4, 10, 25, 24, 8, 15, 55, 85, 60, 16, 21, 105, 231, 258, 144, 32, 28, 182, 532, 833, 728, 336, 64, 36, 294, 1092, 2241, 2720, 1952, 768, 128, 45, 450, 2058, 5301, 8361, 8280, 5040, 1728, 256, 55, 660, 3630, 11385, 22363, 28610, 23920 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column 1: triangular numbers, A000217 Coefficient of v(n,x):  2^(n-1) Row sums:  A035344 Alternating row sums: 1,1,1,1,1,1,1,1,1,... For a discussion and guide to related arrays, see A208510. Appears to be the reversed row polynomials of A165241 with the unit diagonal removed. If so, the o.g.f. is [1-(1+y)x]/[1-2(1+y)x+(1+y)x^2] - 1/(1-x) and the triangular matrix here may be formed by adding each column of the matrix of A056242, presented in the example section with the additional zeros, to its subsequent column with the first row ignored. - Tom Copeland, Jan 09 2017 LINKS FORMULA u(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1, v(n,x)=(x+1)*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 3....2 6....9....4 10...25...24...8 15...55...85...60...16 First three polynomials v(n,x): 1, 3 + 2x, 6 + 9x +4x^2 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1; v[n_, x_] := (x + 1)*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[%]    (* A210753 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A210754 *) Table[u[n, x] /. x -> 1, {n, 1, z}] (* A007070 *) Table[v[n, x] /. x -> 1, {n, 1, z}] (* A035344 *) CROSSREFS Cf. A210753, A208510. Cf. A056242, A165241. Sequence in context: A122362 A072635 A318049 * A210738 A210601 A197493 Adjacent sequences:  A210751 A210752 A210753 * A210755 A210756 A210757 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 25 2012 STATUS approved

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Last modified October 15 10:15 EDT 2019. Contains 328026 sequences. (Running on oeis4.)