A207635 Triangle of coefficients of polynomials u(n,x) jointly generated with A207636; see the Formula section.
1, 2, 5, 2, 11, 9, 2, 23, 29, 13, 2, 47, 81, 55, 17, 2, 95, 209, 191, 89, 21, 2, 191, 513, 591, 369, 131, 25, 2, 383, 1217, 1695, 1329, 631, 181, 29, 2, 767, 2817, 4607, 4353, 2591, 993, 239, 33, 2, 1535, 6401, 12031, 13313, 9535, 4577, 1471, 305, 37, 2
Offset: 1
Examples
First five rows: 1 2 5....2 11...9....2 23...29...13...2
Crossrefs
Cf. A207636.
Programs
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Mathematica
u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + v[n - 1, x] v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1 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[%] (* A207635 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%] (* A207636 *)
Formula
u(n,x)=u(n-1,x)+v(n-1,x),
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.
Comments