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A208522
Triangle of coefficients of polynomials u(n,x) jointly generated with A208522; see the Formula section.
3
1, 1, 1, 1, 2, 3, 1, 3, 6, 5, 1, 4, 9, 12, 11, 1, 5, 12, 21, 30, 21, 1, 6, 15, 32, 57, 64, 43, 1, 7, 18, 45, 92, 133, 146, 85, 1, 8, 21, 60, 135, 232, 329, 316, 171, 1, 9, 24, 77, 186, 365, 612, 765, 694, 341, 1, 10, 27, 96, 245, 536, 1015, 1512, 1801, 1496, 683
OFFSET
1,5
FORMULA
u(n,x)=u(n-1,x)+x*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
1...1
1...2...3
1...3...6...5
1...4...9...12...11
First five polynomials u(n,x):
1
1 + x
1 + 2x + 3x^2
1 + 3x + 6x^2 + 5x^3
1 + 4x + 9x^2 + 12x^3 + 11x^4
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*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[%] (* A208522 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208523 *)
CROSSREFS
Cf. A208523.
Sequence in context: A117938 A256193 A101912 * A209569 A368158 A176850
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 29 2012
STATUS
approved