A208920 Triangle of coefficients of polynomials v(n,x) jointly generated with A208919; see the Formula section.

1, 2, 3, 3, 7, 7, 4, 12, 26, 19, 5, 18, 62, 85, 47, 6, 25, 120, 235, 264, 123, 7, 33, 205, 515, 879, 803, 311, 8, 42, 322, 980, 2254, 3038, 2358, 803, 9, 52, 476, 1694, 4914, 8708, 10156, 6865, 2047, 10, 63, 672, 2730, 9576, 20958, 32640, 32877, 19588

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..54.

Formula

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

v(n,x)=2x*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
2...3
3...7....7
4...12...26...19
5...18...62...85...47
First five polynomials v(n,x):
1
2 + 3x
3 + 7x + 7x^2
4 + 12x + 26x^2 + 19x^3
5 + 18x + 62x^2 + 85x^3 + 47x^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_] := 2 x*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[%]    (* A208919 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208920 *)

Crossrefs

Cf. A208919, A208510.

Sequence in context: A143444 A108346 A210558 * A210234 A209768 A209169

Adjacent sequences: A208917 A208918 A208919 * A208921 A208922 A208923

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 04 2012

Status

approved