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A208919
Triangle of coefficients of polynomials u(n,x) jointly generated with A208920; see the Formula section.
3
1, 1, 2, 1, 6, 6, 1, 12, 20, 14, 1, 20, 44, 66, 38, 1, 30, 80, 190, 208, 94, 1, 42, 130, 430, 678, 622, 246, 1, 56, 196, 840, 1708, 2380, 1852, 622, 1, 72, 280, 1484, 3668, 6888, 7928, 5338, 1606, 1, 90, 384, 2436, 7056, 16716, 25344, 25650, 15336
OFFSET
1,3
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+2x*v(n-1,x),
v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...2
1...6....6
1...12...20...14
1...20...44...66...38
First five polynomials u(n,x):
1
1 + 2x
1 + 6x + 6x^2
1 + 12x + 20x^2 + 14x^3
1 + 20x + 44x^2 + 66x^3 + 38x^4
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*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[%] (* A208919 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208920 *)
CROSSREFS
Sequence in context: A208909 A229565 A259477 * A347580 A259569 A046651
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 04 2012
STATUS
approved