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A210233 Triangle of coefficients of polynomials u(n,x) jointly generated with A210234; see the Formula section. 3
1, 2, 1, 3, 5, 1, 4, 10, 12, 1, 5, 18, 30, 27, 1, 6, 27, 68, 83, 58, 1, 7, 39, 119, 225, 217, 121, 1, 8, 52, 200, 454, 680, 544, 248, 1, 9, 68, 300, 866, 1566, 1928, 1320, 503, 1, 10, 85, 440, 1450, 3332, 5014, 5216, 3121, 1014, 1, 11, 105, 605, 2350, 6182 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..60.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...1

3...5....1

4...10...12...1

5...18...30...27...1

First three polynomials u(n,x): 1, 2 + x, 3 + 5x + x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*u[n - 1, x] + 2 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[%]      (* A210233 *)

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

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

TableForm[cv]

Flatten[%]      (* A210234 *)

CROSSREFS

Cf. A210234, A208510.

Sequence in context: A030237 A210557 A118243 * A297582 A134081 A134247

Adjacent sequences:  A210230 A210231 A210232 * A210234 A210235 A210236

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 20 2012

STATUS

approved

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Last modified October 19 05:57 EDT 2018. Contains 316336 sequences. (Running on oeis4.)