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

1, 1, 1, 1, 4, 1, 1, 9, 4, 1, 1, 16, 12, 7, 1, 1, 25, 30, 26, 7, 1, 1, 36, 65, 73, 32, 10, 1, 1, 49, 126, 175, 113, 52, 10, 1, 1, 64, 224, 378, 332, 199, 61, 13, 1, 1, 81, 372, 756, 852, 634, 277, 87, 13, 1, 1, 100, 585, 1422, 1974, 1779, 1024, 421, 99, 16, 1, 1, 121

Offset

1,5

Links

Table of n, a(n) for n=1..68.

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
1...1
1...4....1
1...9....4....1
1...16...12...7...1
First five polynomials u(n,x):
1
1 + x
1 + 4x + 1x^2
1 + 9x + 4x^2 + x^3
1 + 16x + 12x^2 + 7x^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. A208607.

Sequence in context: A231987 A376784 A235214 * A136100 A244811 A183153

Adjacent sequences: A208603 A208604 A208605 * A208607 A208608 A208609

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 29 2012

Extensions

a(68) corrected by Georg Fischer, Sep 03 2021

Status

approved