A208612 Triangle of coefficients of polynomials u(n,x) jointly generated with A208613; see the Formula section.

1, 1, 1, 1, 4, 2, 1, 9, 9, 3, 1, 16, 26, 19, 5, 1, 25, 60, 70, 38, 8, 1, 36, 120, 197, 167, 73, 13, 1, 49, 217, 469, 553, 375, 137, 21, 1, 64, 364, 994, 1528, 1427, 803, 252, 34, 1, 81, 576, 1932, 3714, 4476, 3449, 1661, 457, 55, 1, 100, 870, 3510, 8196

Offset

1,5

Links

Table of n, a(n) for n=1..60.

Formula

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

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

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

Example

First five rows:
1
1...1
1...4....2
1...9....9....3
1...16...26...19...5
First five polynomials u(n,x):
1
1 + x
1 + 4x + 2x^2
1 + 9x + 9x^2 + 3x^3
1 + 16x + 26x^2 + 19x^3 + 5x^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] + (x + 1)*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[%]  (* A208612 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A208613 *)

Crossrefs

Cf. A208613.

Sequence in context: A177347 A101020 A160905 * A183157 A211957 A338397

Adjacent sequences: A208609 A208610 A208611 * A208613 A208614 A208615

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 01 2012

Status

approved