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A209565
Triangle of coefficients of polynomials u(n,x) jointly generated with A209566; see the Formula section.
3
1, 1, 1, 1, 4, 1, 1, 4, 11, 1, 1, 4, 14, 26, 1, 1, 4, 14, 45, 57, 1, 1, 4, 14, 48, 133, 120, 1, 1, 4, 14, 48, 161, 366, 247, 1, 1, 4, 14, 48, 164, 520, 952, 502, 1, 1, 4, 14, 48, 164, 557, 1604, 2371, 1013, 1, 1, 4, 14, 48, 164, 560, 1863, 4724, 5711, 2036, 1, 1, 4
OFFSET
1,5
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+v(n-1,x),
v(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...1
1...4....1
1...4....11...1
1...4...14...26...1
First three polynomials v(n,x): 1, 1 + x, 1 + 4x + x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
v[n_, x_] := 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[%] (* A209565 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209566 *)
CROSSREFS
Sequence in context: A124258 A001638 A133826 * A122185 A350000 A193752
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 10 2012
STATUS
approved