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A210865 Triangle of coefficients of polynomials v(n,x) jointly generated with A210864; see the Formula section. 3
1, 2, 2, 6, 7, 3, 12, 21, 18, 5, 20, 61, 75, 42, 8, 30, 151, 262, 231, 93, 13, 42, 323, 829, 1025, 656, 196, 21, 56, 617, 2330, 3935, 3607, 1742, 401, 34, 72, 1081, 5815, 13578, 16849, 11723, 4380, 799, 55, 90, 1771, 13070, 42167, 69475, 65727 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For n>1, row n starts with n(n-1) 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..51.

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....2

6....7....3

12...21...18...5

20...61...75...34...8

First three polynomials v(n,x): 1, 2 + 2x, 6 + 7x + 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)*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. A210864, A208510.

Sequence in context: A247525 A305295 A174789 * A210861 A062073 A021445

Adjacent sequences:  A210862 A210863 A210864 * A210866 A210867 A210868

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 28 2012

STATUS

approved

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Last modified October 23 14:22 EDT 2019. Contains 328345 sequences. (Running on oeis4.)