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A210864 Triangle of coefficients of polynomials u(n,x) jointly generated with A210865; see the Formula section. 3
1, 2, 1, 3, 3, 2, 4, 9, 9, 3, 5, 21, 30, 21, 5, 6, 41, 91, 96, 47, 8, 7, 71, 242, 358, 278, 101, 13, 8, 113, 565, 1187, 1303, 757, 209, 21, 9, 169, 1182, 3517, 5238, 4364, 1951, 422, 34, 10, 241, 2263, 9332, 18816, 21213, 13674, 4802, 833, 55, 11, 331 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers).

Column 2:  A064999

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..57.

FORMULA

u(n,x)=u(n-1,x)+x*v(n-1,x)+1,

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

3...3....2

4...9....9....3

5...21...30...21...5

First three polynomials u(n,x): 1, 2 + x, 3 + 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] + 1;

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[%]   (* A210864 *)

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]   (* A210865 *)

CROSSREFS

Cf. A210865, A208510.

Sequence in context: A133341 A111492 A319254 * A144305 A138635 A128182

Adjacent sequences:  A210861 A210862 A210863 * A210865 A210866 A210867

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 28 2012

STATUS

approved

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Last modified October 16 23:50 EDT 2019. Contains 328103 sequences. (Running on oeis4.)