A210200 Triangle of coefficients of polynomials v(n,x) jointly generated with A210199; see the Formula section.

1, 2, 2, 4, 5, 2, 7, 12, 7, 2, 12, 25, 21, 9, 2, 20, 50, 53, 32, 11, 2, 33, 96, 124, 94, 45, 13, 2, 54, 180, 273, 250, 150, 60, 15, 2, 88, 331, 577, 617, 445, 223, 77, 17, 2, 143, 600, 1181, 1444, 1212, 728, 315, 96, 19, 2, 232, 1075, 2358, 3242, 3101, 2163

Offset

1,2

Comments

Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...

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

Links

Table of n, a(n) for n=1..61.

Formula

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

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

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

Example

First five rows:
1
2....2
4....5....2
7....12...7....2
12...25...21...9...2
First three polynomials v(n,x): 1, 2 + 2x , 4 + 5x + 2x^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_] := (x + 1)*u[n - 1, x] + 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[%]   (* A210199 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210200 *)

Crossrefs

Cf. A210199, A208510.

Sequence in context: A109295 A211188 A057899 * A119989 A137605 A328728

Adjacent sequences: A210197 A210198 A210199 * A210201 A210202 A210203

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 18 2012

Status

approved