A210756 Triangle of coefficients of polynomials v(n,x) jointly generated with A210755; see the Formula section.

1, 3, 2, 6, 10, 5, 10, 30, 33, 12, 15, 70, 127, 100, 29, 21, 140, 371, 472, 291, 70, 28, 252, 910, 1656, 1624, 822, 169, 36, 420, 1974, 4800, 6640, 5294, 2273, 408, 45, 660, 3906, 12144, 22166, 24702, 16589, 6184, 985, 55, 990, 7194, 27720, 63954

Offset

1,2

Comments

Column 1: triangular numbers, A000217

Coefficient of v(n,x): A000129(n)

Row sums: A002450

Alternating row sums: 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..50.

Formula

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

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
6....10...5
10...30...33....12
15...70...127...100...29
First three polynomials v(n,x): 1, 3 + 2x, 6 + 10x + 5x^2

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
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[%]    (* A210755 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210756 *)
Table[u[n, x] /. x -> 1, {n, 1, z}] (* A002450 *)
Table[v[n, x] /. x -> 1, {n, 1, z}] (* A002450 *)

Crossrefs

Cf. A210755, A208510.

Sequence in context: A245609 A365789 A072765 * A210748 A331889 A369247

Adjacent sequences: A210753 A210754 A210755 * A210757 A210758 A210759

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 25 2012

Status

approved