login
A209750
Triangle of coefficients of polynomials v(n,x) jointly generated with A209749; see the Formula section.
3
1, 2, 1, 2, 4, 1, 3, 6, 7, 1, 3, 11, 15, 11, 1, 4, 14, 32, 32, 16, 1, 4, 21, 51, 79, 61, 22, 1, 5, 25, 84, 152, 174, 107, 29, 1, 5, 34, 118, 277, 393, 352, 176, 37, 1, 6, 39, 172, 447, 796, 915, 666, 275, 46, 1, 6, 50, 225, 705, 1446, 2060, 1965, 1193, 412, 56, 1
OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=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...1
2...4....1
3...6....7....1
3...11...15...11...1
MATHEMATICA
First three polynomials v(n, x): 1, 2 + x , 2 + 4x + x^2.
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := 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[%] (* A209749 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209750 *)
CROSSREFS
Sequence in context: A165092 A306915 A270743 * A156042 A287691 A227926
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 14 2012
STATUS
approved