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A207624 Triangle of coefficients of polynomials u(n,x) jointly generated with A102662; see the Formula section. 3
1, 2, 3, 3, 4, 8, 3, 5, 15, 14, 3, 6, 24, 37, 20, 3, 7, 35, 76, 71, 26, 3, 8, 48, 135, 184, 117, 32, 3, 9, 63, 218, 395, 372, 175, 38, 3, 10, 80, 329, 748, 951, 664, 245, 44, 3, 11, 99, 472, 1295, 2094, 1987, 1084, 327, 50, 3, 12, 120, 651, 2096, 4137, 5032 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
u(n,x)=u(n-1,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. u=A207624; v=A102662.
EXAMPLE
First five rows:
1
2
3...3
4...8....3
5...15...14...3
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_] := 2 x*u[n - 1, x] + x*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[%] (* A207624 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A102662 *)
CROSSREFS
Cf. A102662.
Sequence in context: A140514 A240209 A047079 * A203990 A238812 A227269
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Feb 20 2012
STATUS
approved

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Last modified April 19 16:52 EDT 2024. Contains 371794 sequences. (Running on oeis4.)