A208512 Triangle of coefficients of polynomials v(n,x) jointly generated with A208511; see the Formula section.
1, 2, 2, 2, 5, 4, 2, 7, 12, 8, 2, 9, 21, 28, 16, 2, 11, 32, 58, 64, 32, 2, 13, 45, 101, 152, 144, 64, 2, 15, 60, 159, 296, 384, 320, 128, 2, 17, 77, 234, 513, 824, 944, 704, 256, 2, 19, 96, 328, 822, 1554, 2208, 2272, 1536, 512, 2, 21, 117, 443, 1244, 2685
Offset: 1
Examples
First five rows: 1 2...2 2...5...4 2...7...12...8 2...9...21...28...16 First five polynomials v(n,x): 1 2 + 2x 2 + 5x + 4x^2 2 + 7x + 12x^2 + 8x^3 2 + 9x + 21x^2 + 28x^3 + 16x^4
Crossrefs
Cf. A208511.
Programs
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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] + 2 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[%] (* A208511 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%] (* A208512 *)
Formula
u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
Comments