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A210858
Triangle of coefficients of polynomials u(n,x) jointly generated with A210859; see the Formula section.
3
1, 1, 1, 1, 3, 2, 1, 6, 8, 3, 1, 10, 24, 20, 5, 1, 15, 59, 82, 45, 8, 1, 21, 125, 271, 251, 98, 13, 1, 28, 237, 765, 1073, 701, 204, 21, 1, 36, 413, 1898, 3860, 3802, 1842, 414, 34, 1, 45, 674, 4235, 12115, 17011, 12325, 4589, 820, 55, 1, 55, 1044, 8662
OFFSET
1,5
COMMENTS
Row n starts with 1 and ends with F(n), where F=A000045 (Fibonacci numbers).
Alternating row sums: 1,0,0,0,0,0,0,0,...
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=(x+n)*u(n-1,x)+x*v(n-1,x),
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...1
1...3....2
1...6....8....3
1...10...24...20...5
First three polynomials u(n,x): 1, 1 + x, 1 + 3x + 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];
v[n_, x_] := (x + n)*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[%] (* A210858 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210859 *)
CROSSREFS
Sequence in context: A257558 A370470 A202390 * A114586 A052174 A227790
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 28 2012
STATUS
approved