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A210189 Triangle of coefficients of polynomials u(n,x) jointly generated with A210190; see the Formula section. 3
1, 3, 6, 2, 10, 10, 15, 30, 4, 21, 70, 28, 28, 140, 112, 8, 36, 252, 336, 72, 45, 420, 840, 360, 16, 55, 660, 1848, 1320, 176, 66, 990, 3696, 3960, 1056, 32, 78, 1430, 6864, 10296, 4576, 416, 91, 2002, 12012, 24024, 16016, 2912, 64, 105, 2730, 20020 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 1:  triangular numbers: A000217

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

LINKS

Table of n, a(n) for n=1..52.

FORMULA

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

v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,

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

EXAMPLE

First five rows:

1

3

6....2

10...10

15...30...4

First three polynomials u(n,x): 1, 3, 6 + 2x.

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;

v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;

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[%]   (* A210189 *)

Table[Expand[v[n, x]], {n, 1, z}]

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

TableForm[cv]

Flatten[%]   (* A210190 *)

CROSSREFS

Cf. A210190, A208510.

Sequence in context: A266971 A257106 A210187 * A257506 A210035 A210199

Adjacent sequences:  A210186 A210187 A210188 * A210190 A210191 A210192

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Mar 18 2012

STATUS

approved

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)