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A209560
Triangle of coefficients of polynomials v(n,x) jointly generated with A209559; see the Formula section.
3
1, 3, 1, 5, 5, 1, 9, 12, 7, 1, 15, 29, 22, 9, 1, 25, 61, 66, 35, 11, 1, 41, 124, 166, 125, 51, 13, 1, 67, 241, 394, 365, 211, 70, 15, 1, 109, 457, 877, 988, 701, 329, 92, 17, 1, 177, 848, 1877, 2472, 2129, 1225, 484, 117, 19, 1, 287, 1549, 3884, 5880, 5909
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)+(x+1)*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3....1
5....5....1
9....12...7....1
15...29...22...9...1
First three polynomials v(n,x): 1, 3 + x , 5 + 5x + 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_] := 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[%] (* A209559 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209560 *)
CROSSREFS
Sequence in context: A376102 A343510 A344725 * A211977 A072919 A273171
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 10 2012
STATUS
approved