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A209160
Triangle of coefficients of polynomials u(n,x) jointly generated with A209161; see the Formula section.
3
1, 2, 1, 3, 6, 4, 4, 13, 20, 10, 5, 22, 52, 62, 28, 6, 33, 104, 192, 192, 76, 7, 46, 180, 444, 680, 584, 208, 8, 61, 284, 870, 1776, 2328, 1760, 568, 9, 78, 420, 1530, 3876, 6768, 7776, 5256, 1552, 10, 97, 592, 2492, 7504, 16260, 24864, 25464, 15584
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)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...1
3...6....4
4...13...20...10
5...22...52...62...28
First three polynomials v(n,x): 1, 2 + x, 3 + 6x + 4x^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] + 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[%] (* A209160 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209161 *)
CROSSREFS
Sequence in context: A347297 A133904 A245182 * A371418 A340406 A257881
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 07 2012
STATUS
approved