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A210860
Triangle of coefficients of polynomials u(n,x) jointly generated with A210861; see the Formula section of A210861.
3
1, 2, 1, 4, 5, 2, 10, 18, 12, 3, 26, 64, 62, 28, 5, 76, 230, 286, 183, 60, 8, 232, 846, 1298, 1073, 503, 126, 13, 764, 3220, 5832, 5884, 3563, 1288, 255, 21, 2620, 12608, 26436, 31530, 23353, 10956, 3158, 506, 34, 9496, 51084, 121276, 166630
OFFSET
1,2
COMMENTS
Row n ends with F(n), where F=A000045 (Fibonacci numbers).
Column 1: A000085
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+(x+1)*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
2 1
4 5 2
10 18 12 3
26 64 62 28 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 + 1)*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[%] (* A210860 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210861 *)
CROSSREFS
Sequence in context: A038719 A376286 A125751 * A381531 A099492 A359708
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 28 2012
EXTENSIONS
Definition clarified by Alonso del Arte and Harvey P. Dale, Dec 17 2012
STATUS
approved