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A209576
Triangle of coefficients of polynomials v(n,x) jointly generated with A209575; see the Formula section.
3
1, 1, 4, 1, 4, 10, 1, 4, 18, 22, 1, 4, 18, 66, 46, 1, 4, 18, 82, 206, 94, 1, 4, 18, 82, 342, 578, 190, 1, 4, 18, 82, 374, 1274, 1510, 382, 1, 4, 18, 82, 374, 1642, 4294, 3754, 766, 1, 4, 18, 82, 374, 1706, 6726, 13354, 9006, 1534, 1, 4, 18, 82, 374, 1706
OFFSET
1,3
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)=2x*u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...4
1...4...10
1...4...18...22
1...4...18...66...46
First three polynomials v(n,x): 1, 1+4x, 1+4x+10x^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_] := 2 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[%] (* A209575 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209576 *)
CROSSREFS
Sequence in context: A201286 A347221 A208527 * A055886 A132478 A208918
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 11 2012
STATUS
approved