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A209688
Triangle of coefficients of polynomials v(n,x) jointly generated with A115241; see the Formula section.
3
1, 3, 4, 2, 5, 5, 2, 6, 9, 7, 2, 7, 14, 16, 9, 2, 8, 20, 30, 25, 11, 2, 9, 27, 50, 55, 36, 13, 2, 10, 35, 77, 105, 91, 49, 15, 2, 11, 44, 112, 182, 196, 140, 64, 17, 2, 12, 54, 156, 294, 378, 336, 204, 81, 19, 2, 13, 65, 210, 450, 672, 714, 540, 285, 100, 21, 2
OFFSET
1,2
COMMENTS
Alternating row sums: 1,3,2,2,2,2,2,2,2,2,2,2,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+x*v(n-1,x),
v(n,x)=u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3...1
4...2...3
5...5...2
6...9...7...2
First three polynomials v(n,x): 1, 3 + x , 4 + 2x + 3x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
v[n_, 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[%] (* A115241 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209688 *)
CROSSREFS
Sequence in context: A246832 A133570 A117041 * A143939 A197269 A201905
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 12 2012
STATUS
approved