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A209558
Triangle of coefficients of polynomials v(n,x) jointly generated with A209557; see the Formula section.
3
1, 2, 2, 2, 5, 4, 3, 7, 11, 8, 3, 13, 21, 23, 16, 4, 15, 44, 57, 47, 32, 4, 24, 60, 129, 145, 95, 64, 5, 26, 108, 207, 346, 353, 191, 128, 5, 38, 130, 405, 646, 875, 833, 383, 256, 6, 40, 212, 545, 1345, 1877, 2124, 1921, 767, 512, 6, 55, 240, 965, 2021
OFFSET
1,2
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)=u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
2...5...4
3...7...11...8
3...13...21...23...16
First three polynomials v(n,x): 1, 2 + 2x , 2+ 5x + 4x^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_] := 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[%] (* A209557 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209558 *)
CROSSREFS
Sequence in context: A210562 A208512 A208908 * A209772 A370164 A147293
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 10 2012
STATUS
approved