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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 (list; table; graph; refs; listen; history; text; internal format)
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.

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.

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.

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 *)

LINKS

Table of n, a(n) for n=1..49.

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.

CROSSREFS

Cf. A210861, A208510.

Sequence in context: A209141 A038719 A125751 * A099492 A144203 A239806

Adjacent sequences:  A210857 A210858 A210859 * A210861 A210862 A210863

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

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Last modified October 16 23:30 EDT 2019. Contains 328103 sequences. (Running on oeis4.)