A210858 Triangle of coefficients of polynomials u(n,x) jointly generated with A210859; see the Formula section.

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.

Links

Table of n, a(n) for n=1..59.

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

Cf. A210806, A208510.

Sequence in context: A257558 A370470 A202390 * A114586 A052174 A227790

Adjacent sequences: A210855 A210856 A210857 * A210859 A210860 A210861

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 28 2012

Status

approved