A208930 Triangle of coefficients of polynomials v(n,x) jointly generated with A208930; see the Formula section.

1, 2, 3, 2, 7, 8, 2, 11, 26, 22, 2, 15, 52, 88, 60, 2, 19, 86, 214, 288, 164, 2, 23, 128, 416, 820, 916, 448, 2, 27, 178, 710, 1824, 2984, 2856, 1224, 2, 31, 236, 1112, 3500, 7464, 10464, 8768, 3344, 2, 35, 302, 1638, 6080, 15884, 29040, 35664, 26592

Offset

1,2

Comments

For a discussion and guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..54.

Formula

u(n,x)=u(n-1,x)+2x*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...7....8
2...11...26...22
2...15...52...88...60
First five polynomials v(n,x):
1
2 + 3x
2 + 7x + 8x^2
2 + 11x + 26x^2 + 22x^3
2 + 15x + 52x^2 + 88x^3 + 60x^4

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 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[%]    (* A208909 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208930 *)

Crossrefs

Cf. A208909, A208510.

Sequence in context: A122697 A129022 A210564 * A122076 A209774 A271322

Adjacent sequences: A208927 A208928 A208929 * A208931 A208932 A208933

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 04 2012

Status

approved