A208522 Triangle of coefficients of polynomials u(n,x) jointly generated with A208522; see the Formula section.

1, 1, 1, 1, 2, 3, 1, 3, 6, 5, 1, 4, 9, 12, 11, 1, 5, 12, 21, 30, 21, 1, 6, 15, 32, 57, 64, 43, 1, 7, 18, 45, 92, 133, 146, 85, 1, 8, 21, 60, 135, 232, 329, 316, 171, 1, 9, 24, 77, 186, 365, 612, 765, 694, 341, 1, 10, 27, 96, 245, 536, 1015, 1512, 1801, 1496, 683

Offset

1,5

Links

Table of n, a(n) for n=1..66.

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...1
1...2...3
1...3...6...5
1...4...9...12...11
First five polynomials u(n,x):
1
1 + x
1 + 2x + 3x^2
1 + 3x + 6x^2 + 5x^3
1 + 4x + 9x^2 + 12x^3 + 11x^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. A208523.

Sequence in context: A117938 A256193 A101912 * A209569 A368158 A176850

Adjacent sequences: A208519 A208520 A208521 * A208523 A208524 A208525

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 29 2012

Status

approved