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A207620
Triangle of coefficients of polynomials u(n,x) jointly generated with A207621; see the Formula section.
3
1, 2, 4, 2, 7, 8, 2, 11, 21, 12, 2, 16, 45, 43, 16, 2, 22, 85, 119, 73, 20, 2, 29, 147, 280, 249, 111, 24, 2, 37, 238, 588, 705, 451, 157, 28, 2, 46, 366, 1134, 1749, 1496, 741, 211, 32, 2, 56, 540, 2046, 3927, 4290, 2821, 1135, 273, 36, 2, 67, 770, 3498
OFFSET
1,2
FORMULA
u(n,x)=u(n-1,x)+v(n-1,x),
v(n,x)=x*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
2
4...2
7...8...2
11...21...12...2
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A207620 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A207621 *)
CROSSREFS
Cf. A207621.
Sequence in context: A214789 A207631 A207612 * A354766 A207622 A335573
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Feb 20 2012
STATUS
approved