A208607 Triangle of coefficients of polynomials v(n,x) jointly generated with A208606; see the Formula section.

1, 3, 1, 5, 3, 1, 7, 8, 6, 1, 9, 18, 19, 6, 1, 11, 35, 47, 25, 9, 1, 13, 61, 102, 81, 42, 9, 1, 15, 98, 203, 219, 147, 51, 12, 1, 17, 148, 378, 520, 435, 216, 74, 12, 1, 19, 213, 666, 1122, 1145, 747, 334, 86, 15, 1, 21, 295, 1119, 2250, 2753, 2233, 1245, 450

Offset

1,2

Comments

Alternating rows sums: 1,2,3,4,5,6,7,8,...

Links

Table of n, a(n) for n=1..63.

Formula

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

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

where u(1,x)=1, v(1,x)=1.

Example

First five rows:
1
3...1
5...3...1
7...8...6...1
9...18...19...6...1
First five polynomials v(n,x):
1
3 + x
5 + 3x + x^2
7 + 8x + 6x^2 + x^3
9 + 18x + 19x^2 + 6x^3 + x^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] + 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[%]  (* A208606 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A208607 *)

Crossrefs

Cf. A208606.

Sequence in context: A258207 A133094 A300437 * A159291 A122510 A102662

Adjacent sequences: A208604 A208605 A208606 * A208608 A208609 A208610

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 29 2012

Status

approved