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A209754 Triangle of coefficients of polynomials v(n,x) jointly generated with A209753; see the Formula section. 3
1, 3, 1, 5, 6, 1, 9, 16, 10, 1, 15, 39, 38, 15, 1, 25, 84, 117, 76, 21, 1, 41, 172, 308, 286, 136, 28, 1, 67, 337, 744, 894, 612, 225, 36, 1, 109, 642, 1685, 2496, 2228, 1191, 351, 45, 1, 177, 1196, 3646, 6423, 7088, 4978, 2157, 523, 55, 1, 287, 2191 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=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
3....1
5....6....1
9....16...10...1
15...39...38...15...1
First three polynomials v(n,x): 1, 3 + x , 5 + 6x + x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, 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[%] (* A209753 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209754 *)
CROSSREFS
Sequence in context: A108283 A208904 A344479 * A140950 A256504 A205713
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 14 2012
STATUS
approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)