login
A210190
Triangle of coefficients of polynomials v(n,x) jointly generated with A210189; see the Formula section.
3
1, 2, 2, 3, 8, 4, 20, 4, 5, 40, 24, 6, 70, 84, 8, 7, 112, 224, 64, 8, 168, 504, 288, 16, 9, 240, 1008, 960, 160, 10, 330, 1848, 2640, 880, 32, 11, 440, 3168, 6336, 3520, 384, 12, 572, 5148, 13728, 11440, 2496, 64, 13, 728, 8008, 27456, 32032, 11648
OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+v(n-1,x)+1,
v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
3...8
4...20...4
5...40...24
First three polynomials v(n,x): 1, 2 + 2x , 3 + 8x.
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] + 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[%] (* A210189 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210190 *)
CROSSREFS
Sequence in context: A176383 A100551 A267667 * A070267 A205374 A056762
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 18 2012
STATUS
approved