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A210863 Triangle of coefficients of polynomials v(n,x) jointly generated with A210862; see the Formula section. 3
1, 1, 2, 4, 5, 3, 9, 13, 13, 5, 16, 37, 47, 32, 8, 25, 96, 152, 147, 73, 13, 36, 217, 469, 587, 432, 158, 21, 49, 435, 1344, 2127, 2090, 1183, 330, 34, 64, 793, 3487, 7186, 8979, 6965, 3064, 669, 55, 81, 1342, 8179, 22544, 35296, 35304, 21754, 7577 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For n>1, row n starts with (n-1)^2 and ends with F(n+1), where F=A000045 (Fibonacci numbers).

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

LINKS

Table of n, a(n) for n=1..53.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1....2

4....5....3

9....13...13...5

16...37...47...32...8

First three polynomials v(n,x): 1, 1 + 2x, 4 + 5x + 3x^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 - 1)*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[%]   (* A210862 *)

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

TableForm[cv]

Flatten[%]   (* A210863 *)

CROSSREFS

Cf. A210862, A208510.

Sequence in context: A097292 A269780 A038776 * A245816 A118461 A266408

Adjacent sequences:  A210860 A210861 A210862 * A210864 A210865 A210866

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 28 2012

STATUS

approved

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Last modified October 16 16:13 EDT 2019. Contains 328101 sequences. (Running on oeis4.)