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

1, 2, 3, 3, 11, 7, 4, 26, 38, 17, 5, 50, 124, 121, 41, 6, 85, 314, 499, 362, 99, 7, 133, 679, 1555, 1805, 1043, 239, 8, 196, 1316, 4054, 6672, 6096, 2926, 577, 9, 276, 2352, 9318, 20326, 26048, 19610, 8049, 1393, 10, 375, 3948, 19482, 53932, 90706

Offset

1,2

Comments

Row n starts with n and ends with A001333(n).

Column 2: A051925

Row sums: A002450

Alternating row sums: 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..51.

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
2...3
3...11...7
4...26...38....17
5...50...124...121...41
First three polynomials u(n,x): 1, 2 + 3x, 3 + 11x + 7x^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. A210754, A208510.

Sequence in context: A155758 A009097 A210194 * A219224 A265532 A112858

Adjacent sequences: A210752 A210753 A210754 * A210756 A210757 A210758

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 25 2012

Status

approved