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A208520
Triangle of coefficients of polynomials u(n,x) jointly generated with A208521; see the Formula section.
3
1, 1, 1, 1, 3, 2, 1, 6, 6, 2, 1, 10, 12, 10, 4, 1, 15, 20, 30, 20, 4, 1, 21, 30, 70, 60, 28, 8, 1, 28, 42, 140, 140, 112, 56, 8, 1, 36, 56, 252, 280, 336, 224, 72, 16, 1, 45, 72, 420, 504, 840, 672, 360, 144, 16, 1, 55, 90, 660, 840, 1848, 1680, 1320, 720, 176
OFFSET
1,5
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...1
1...3...2
1...6...6...2
1...10...12...10...4
First five polynomials u(n,x):
1
1 + x
1 + 3x + 2x^2
1 + 6x + 6x^2 + 2x^3
1 + 10x + 12x^2 + 10x^3 + 4x^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] + 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[%] (* A208520 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208521 *)
CROSSREFS
Cf. A208521.
Sequence in context: A113655 A177977 A365743 * A114155 A192018 A079513
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 28 2012
STATUS
approved