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A209568
Triangle of coefficients of polynomials v(n,x) jointly generated with A209567; see the Formula section.
3
1, 2, 2, 3, 5, 3, 4, 10, 11, 4, 5, 17, 28, 21, 5, 6, 26, 58, 67, 36, 6, 7, 37, 105, 166, 142, 57, 7, 8, 50, 173, 350, 416, 274, 85, 8, 9, 65, 266, 659, 1011, 940, 491, 121, 9, 10, 82, 388, 1141, 2156, 2612, 1955, 829, 166, 10, 11, 101, 543, 1852, 4172, 6265
OFFSET
1,2
COMMENTS
Row n begins and ends with n.
Column 2: (n-1)^2, for n>1.
Alternating row sums: 1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,...
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)+(x+1)*v(n-1,x) +1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
3...5...3
4...10...11...4
5...17...28...21...5
First three polynomials v(n,x): 1, 2+2x, 3+5x+3x^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] + (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[%] (* A209567 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209568 *)
CROSSREFS
Sequence in context: A210232 A047666 A285935 * A227641 A295097 A295551
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 10 2012
STATUS
approved