A210194 Triangle of coefficients of polynomials v(n,x) jointly generated with A210193; see the Formula section.

1, 2, 3, 3, 11, 3, 4, 26, 20, 3, 5, 50, 74, 29, 3, 6, 85, 204, 149, 38, 3, 7, 133, 469, 547, 251, 47, 3, 8, 196, 952, 1618, 1160, 380, 56, 3, 9, 276, 1764, 4110, 4234, 2124, 536, 65, 3, 10, 375, 3048, 9318, 13036, 9262, 3520, 719, 74, 3, 11, 495, 4983

Offset

1,2

Comments

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

Links

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

Formula

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

v(n,x)=2x*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...3
4...26...20...3
5...50...74...29...3
First three polynomials v(n,x): 1, 2 + 3x , 3 + 11x + 3x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 2 x*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[%]   (* A210193 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A210194 *)

Crossrefs

Cf. A210193, A208510.

Sequence in context: A117030 A155758 A009097 * A210755 A219224 A265532

Adjacent sequences: A210191 A210192 A210193 * A210195 A210196 A210197

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 18 2012

Status

approved