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A209152
Triangle of coefficients of polynomials u(n,x) jointly generated with A208339; see the Formula section.
2
1, 2, 1, 3, 5, 3, 4, 10, 14, 7, 5, 16, 32, 37, 17, 6, 23, 58, 97, 98, 41, 7, 31, 93, 197, 287, 257, 99, 8, 40, 138, 348, 642, 830, 670, 239, 9, 50, 194, 562, 1234, 2024, 2360, 1737, 577, 10, 61, 262, 852, 2148, 4198, 6220, 6617, 4482, 1393, 11, 73, 343
OFFSET
1,2
COMMENTS
Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...1
3...5....3
4...10...14...7
5...16...32...37...17
First three polynomials v(n,x): 1, 2 + x, 3 + 5x + 3x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := x*u[n - 1, x] + 2 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[%] (* A209152 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208339 *)
CROSSREFS
Sequence in context: A060083 A069931 A373534 * A209158 A209135 A258236
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 07 2012
STATUS
approved