A208611 Triangle of coefficients of polynomials v(n,x) jointly generated with A208610; see the Formula section.

1, 2, 3, 2, 6, 7, 2, 8, 18, 17, 2, 10, 30, 52, 41, 2, 12, 44, 102, 146, 99, 2, 14, 60, 170, 328, 402, 239, 2, 16, 78, 258, 610, 1014, 1090, 577, 2, 18, 98, 368, 1016, 2076, 3044, 2920, 1393, 2, 20, 120, 502, 1572, 3756, 6792, 8932, 7746, 3363, 2, 22, 144

Offset

1,2

Links

Table of n, a(n) for n=1..58.

Formula

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

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

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

Example

First five rows:
1
2...3
2...6....7
2...8....18...17
2...10...30...52...41
First five polynomials v(n,x):
1
2 + 3x
2 + 6x + 7x^2
2 + 8x + 18x^2 + 17x^3
2 + 10x + 30x^2 + 52x^3 + 41x^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] + 2 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[%]  (* A208610 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A208611 *)

Crossrefs

Cf. A208610.

Sequence in context: A348083 A306156 A276125 * A209582 A158279 A153984

Adjacent sequences: A208608 A208609 A208610 * A208612 A208613 A208614

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 01 2012

Status

approved