A209581 Triangle of coefficients of polynomials u(n,x) jointly generated with A209582; see the Formula section.

1, 1, 1, 2, 4, 1, 2, 8, 11, 1, 3, 12, 25, 26, 1, 3, 19, 51, 71, 57, 1, 4, 24, 88, 180, 190, 120, 1, 4, 34, 136, 348, 566, 486, 247, 1, 5, 40, 206, 628, 1238, 1648, 1199, 502, 1, 5, 53, 282, 1034, 2526, 4070, 4545, 2873, 1013, 1, 6, 60, 395, 1600, 4556, 9208

Offset

1,4

Comments

For a discussion and guide to related arrays, see A208510.

Links

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

Formula

u(n,x)=x*u(n-1,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
2...4....1
2...8....11...1
3...12...25...26...1
First three polynomials v(n,x): 1, 1 + x, 2 + 4x + x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, 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[%]   (* A209581 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209582 *)

Crossrefs

Cf. A209582, A208510.

Sequence in context: A333651 A131398 A249307 * A342053 A050980 A053451

Adjacent sequences: A209578 A209579 A209580 * A209582 A209583 A209584

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 11 2012

Status

approved