login
A208523
Triangle of coefficients of polynomials v(n,x) jointly generated with A208522; see the Formula section.
3
1, 1, 3, 1, 3, 5, 1, 3, 7, 11, 1, 3, 9, 19, 21, 1, 3, 11, 27, 43, 43, 1, 3, 13, 35, 69, 103, 85, 1, 3, 15, 43, 99, 183, 231, 171, 1, 3, 17, 51, 133, 283, 449, 523, 341, 1, 3, 19, 59, 171, 403, 747, 1107, 1155, 683, 1, 3, 21, 67, 213, 543, 1133, 1971, 2637, 2543
OFFSET
1,3
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...3
1...3...5
1...3...7...11
1...3...9...19...21
First five polynomials v(n,x):
1
1 + 3x
1 + 3x + 5x^2
1 + 3x + 7x^2 + 11x^3
1 + 3x + 9x^2 + 19x^3 + 21x^4
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, x] + 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[%] (* A208522 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208523 *)
CROSSREFS
Cf. A208522.
Sequence in context: A294966 A258208 A210952 * A209572 A134231 A225598
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 29 2012
STATUS
approved