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A209562
Triangle of coefficients of polynomials v(n,x) jointly generated with A209561; see the Formula section.
3
1, 2, 1, 3, 2, 1, 4, 4, 3, 1, 5, 7, 7, 4, 1, 6, 11, 14, 11, 5, 1, 7, 16, 25, 25, 16, 6, 1, 8, 22, 41, 50, 41, 22, 7, 1, 9, 29, 63, 91, 91, 63, 29, 8, 1, 10, 37, 92, 154, 182, 154, 92, 37, 9, 1, 11, 46, 129, 246, 336, 336, 246, 129, 46, 10, 1, 12, 56, 175, 375, 582, 672
OFFSET
1,2
COMMENTS
Alternating row sums: 1,1,2,2,2,2,2,2,2,2,2,2,2,2,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+v(n-1,x),
v(n,x)=x*u(n-1,x)+v(n-1,x) +1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...1
3...2...1
4...4...3...1
5...7...7...4...1
First three polynomials v(n,x): 1, 3 + x , 5 + 5x + x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
v[n_, x_] := 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[%] (* A209561 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209562 *)
CROSSREFS
Sequence in context: A361043 A181847 A366986 * A259344 A239030 A165999
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 10 2012
STATUS
approved