A208613 Triangle of coefficients of polynomials v(n,x) jointly generated with A208612; see the Formula section.

1, 3, 2, 5, 7, 3, 7, 17, 16, 5, 9, 34, 51, 33, 8, 11, 60, 127, 129, 65, 13, 13, 97, 272, 386, 302, 124, 21, 15, 147, 525, 975, 1052, 666, 231, 34, 17, 212, 938, 2186, 3049, 2646, 1409, 423, 55, 19, 294, 1578, 4482, 7757, 8650, 6285, 2887, 764, 89, 21

Offset

1,2

Comments

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

Links

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

Formula

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

v(n,x)=(x+1)*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
3...2
5...7....3
7...17...16...3
9...34...51...33...8
First five polynomials v(n,x):
1
3 + 2x
5 + 7x + 3x^2
7 + 17x + 16x^2 + 3x^3
9 + 34x + 51x^2 + 33x^3 + 8x^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_] := (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[%]  (* A208612 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A208613 *)

Crossrefs

Cf. A208612.

Sequence in context: A128224 A125026 A130295 * A209584 A209140 A265903

Adjacent sequences: A208610 A208611 A208612 * A208614 A208615 A208616

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 01 2012

Status

approved