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A209158
Triangle of coefficients of polynomials u(n,x) jointly generated with A209159; see the Formula section.
3
1, 2, 1, 3, 5, 3, 4, 11, 13, 5, 5, 19, 35, 31, 11, 6, 29, 73, 101, 73, 21, 7, 41, 131, 247, 275, 167, 43, 8, 55, 213, 509, 769, 717, 377, 85, 9, 71, 323, 935, 1787, 2255, 1811, 839, 171, 10, 89, 465, 1581, 3657, 5829, 6321, 4461, 1849, 341, 11, 109, 643
OFFSET
1,2
COMMENTS
Alternating row sums: 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)=2x*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
3...5....5
4...11...13...5
5...19...35...31...11
First three polynomials v(n,x): 1, 2 + x, 3 + 5x + 5x^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_] := 2 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[%] (* A209158 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209159 *)
CROSSREFS
Sequence in context: A069931 A373534 A209152 * A209135 A258236 A258244
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 07 2012
STATUS
approved