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A210862
Triangle of coefficients of polynomials u(n,x) jointly generated with A210863; see the Formula section.
3
1, 2, 1, 3, 2, 2, 4, 6, 7, 3, 5, 15, 20, 16, 5, 6, 31, 57, 63, 37, 8, 7, 56, 153, 215, 184, 81, 13, 8, 92, 370, 684, 771, 513, 171, 21, 9, 141, 805, 2028, 2898, 2603, 1354, 351, 34, 10, 205, 1598, 5515, 10084, 11582, 8319, 3415, 703, 55, 11, 286, 2940
OFFSET
1,2
COMMENTS
Row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers).
Column 2: A056520
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x)+1,
v(n,x)=(x+n-1)*u(n-1,x)+x*v(n-1,x),
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...1
3...2....2
4...6....7....3
5...15...20...16...5
First three polynomials u(n,x): 1, 2 + x, 4 + 5x + 2x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 14;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, x_] := (x + n - 1)*u[n - 1, x] + x*v[n - 1, x];
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[%] (* A210862 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210863 *)
CROSSREFS
Sequence in context: A120933 A209756 A210795 * A298675 A365383 A144154
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 28 2012
STATUS
approved