A209584 Triangle of coefficients of polynomials v(n,x) jointly generated with A209583; see the Formula section.

1, 3, 2, 5, 7, 3, 9, 18, 14, 4, 15, 42, 48, 25, 5, 25, 89, 137, 107, 41, 6, 41, 180, 348, 364, 212, 63, 7, 67, 350, 820, 1078, 844, 386, 92, 8, 109, 663, 1827, 2902, 2864, 1773, 659, 129, 9, 177, 1230, 3906, 7284, 8692, 6809, 3453, 1069, 175, 10, 287

Offset

1,2

Comments

Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...

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

Links

Table of n, a(n) for n=1..56.

Formula

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

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

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

Example

First five rows:
1
3....1
5....7....3
9....18...14...4
15...42...48...25...5
First three polynomials v(n,x): 1, 3 + x , 5 + 7x + 3x^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] + (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[%]   (* A209583 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209584 *)

Crossrefs

Cf. A209583, A208510.

Sequence in context: A125026 A130295 A208613 * A209140 A265903 A345420

Adjacent sequences: A209581 A209582 A209583 * A209585 A209586 A209587

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 11 2012

Status

approved