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A209701 Triangle of coefficients of polynomials u(n,x) jointly generated with A209702; see the Formula section. 3
1, 0, 2, 0, 2, 5, 0, 3, 7, 12, 0, 4, 11, 23, 29, 0, 5, 16, 41, 70, 70, 0, 6, 22, 66, 140, 204, 169, 0, 7, 29, 99, 247, 455, 577, 408, 0, 8, 37, 141, 401, 875, 1423, 1597, 985, 0, 9, 46, 193, 613, 1529, 2965, 4321, 4348, 2378, 0, 10, 56, 256, 895, 2495, 5549 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=x*u(n-1,x)+x*v(n-1,x),
v(n,x)=2x*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
0...2
0...2...5
0...3...7....12
0...4...11...23...29
First three polynomials v(n,x): 1, 2x, 2x + 5x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 2 x*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[%] (* A209701 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209702 *)
CROSSREFS
Sequence in context: A052438 A324045 A358405 * A158855 A344908 A005074
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 12 2012
STATUS
approved

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Last modified July 21 02:16 EDT 2024. Contains 374462 sequences. (Running on oeis4.)