A208908 Triangle of coefficients of polynomials v(n,x) jointly generated with A208923; see the Formula section.

1, 2, 2, 2, 5, 4, 2, 9, 15, 8, 2, 13, 33, 37, 16, 2, 17, 59, 103, 91, 32, 2, 21, 93, 221, 297, 213, 64, 2, 25, 135, 407, 739, 807, 491, 128, 2, 29, 185, 677, 1553, 2285, 2105, 1109, 256, 2, 33, 243, 1047, 2907, 5391, 6675, 5319, 2475, 512, 2, 37, 309, 1533

Offset

1,2

Comments

Alternating row sums: 1,0,1,0,1,0,1,0,1,0,1,0,...

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

Links

Table of n, a(n) for n=1..59.

Formula

u(n,x)=u(n-1,x)+2x*v(n-1,x),

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

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

Example

First five rows:
1
2...2
2...5....4
2...9...15...8
2...13...33...37...16
First five polynomials v(n,x):
1
2 + 2x
2 + 5x + 4x^2
2 + 9x + 15x^2 + 8x^3
2 + 13x + 33x^2 + 37x^3 + 16x^4

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := (x + 1)*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[%]    (* A208923 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208908 *)

Crossrefs

Cf. A208923, A208510.

Sequence in context: A246119 A210562 A208512 * A209558 A209772 A370164

Adjacent sequences: A208905 A208906 A208907 * A208909 A208910 A208911

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 04 2012

Status

approved