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A210867 Triangle of coefficients of polynomials v(n,x) jointly generated with A210866; see the Formula section. 4
1, 2, 1, 3, 5, 2, 4, 15, 12, 3, 5, 34, 51, 28, 5, 6, 65, 170, 156, 60, 8, 7, 111, 465, 680, 438, 126, 13, 8, 175, 1092, 2465, 2411, 1145, 255, 21, 9, 260, 2282, 7623, 10968, 7805, 2854, 506, 34, 10, 369, 4356, 20608, 42735, 43440, 23509, 6813, 984, 55 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For n>1, row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers).

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

LINKS

Table of n, a(n) for n=1..55.

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)-x,

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First five rows:

1

2...1

3...5....2

4...15...12...3

5...34...51...28...5

First three polynomials v(n,x): 1, 2 + x, 3 + 5x + 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] - 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[%]   (* A210866 *)

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

TableForm[cv]

Flatten[%]   (* A210867 *)

CROSSREFS

Cf. A210866, A208510.

Sequence in context: A081450 A248408 A210880 * A019588 A193953 A201377

Adjacent sequences:  A210864 A210865 A210866 * A210868 A210869 A210870

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 29 2012

STATUS

approved

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Last modified October 20 20:24 EDT 2019. Contains 328273 sequences. (Running on oeis4.)