A208610 Triangle of coefficients of polynomials u(n,x) jointly generated with A208611; see the Formula section.

1, 1, 1, 1, 3, 3, 1, 5, 9, 7, 1, 7, 17, 25, 17, 1, 9, 27, 55, 69, 41, 1, 11, 39, 99, 171, 187, 99, 1, 13, 53, 159, 341, 515, 501, 239, 1, 15, 69, 237, 599, 1125, 1515, 1329, 577, 1, 17, 87, 335, 967, 2141, 3591, 4373, 3497, 1393, 1, 19, 107, 455, 1469, 3713

Offset

1,5

Links

Table of n, a(n) for n=1..61.

Formula

u(n,x)=u(n-1,x)+x*v(n-1,x),

v(n,x)=(x+1)*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...1
1...3...3
1...5...9...7
1...7...17...25...17
First five polynomials u(n,x):
1
1 + x
1 + 3x + 3x^2
1 + 5x + 9x^2 + 7x^3
1 + 7x + 17x^2 + 25x^3 + 17x^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_] := (x + 1)*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[%]  (* A208610 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A208611 *)

Crossrefs

Cf. A208611.

Sequence in context: A164984 A248810 A339904 * A193823 A071945 A209583

Adjacent sequences: A208607 A208608 A208609 * A208611 A208612 A208613

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 01 2012

Status

approved