A207619 Triangle of coefficients of polynomials v(n,x) jointly generated with A207618; see the Formula section.

1, 1, 3, 1, 4, 6, 1, 5, 11, 12, 1, 6, 17, 28, 24, 1, 7, 24, 51, 68, 48, 1, 8, 32, 82, 142, 160, 96, 1, 9, 41, 122, 255, 376, 368, 192, 1, 10, 51, 172, 417, 744, 960, 832, 384, 1, 11, 62, 233, 639, 1323, 2072, 2384, 1856, 768, 1, 12, 74, 306, 933, 2184, 3974

Offset

1,3

Links

Table of n, a(n) for n=1..62.

Formula

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

Example

First five rows:
1
1...3
1...4...6
1...5...11...12
1...6...17...28...24

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]    (* A207618 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207619 *)

Crossrefs

Cf. A207618.

Sequence in context: A080851 A209518 A108285 * A209694 A286951 A260355

Adjacent sequences: A207616 A207617 A207618 * A207620 A207621 A207622

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 20 2012

Status

approved