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A208520 Triangle of coefficients of polynomials u(n,x) jointly generated with A208521; see the Formula section. 3
1, 1, 1, 1, 3, 2, 1, 6, 6, 2, 1, 10, 12, 10, 4, 1, 15, 20, 30, 20, 4, 1, 21, 30, 70, 60, 28, 8, 1, 28, 42, 140, 140, 112, 56, 8, 1, 36, 56, 252, 280, 336, 224, 72, 16, 1, 45, 72, 420, 504, 840, 672, 360, 144, 16, 1, 55, 90, 660, 840, 1848, 1680, 1320, 720, 176 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..65.

FORMULA

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

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

1...1

1...3...2

1...6...6...2

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

First five polynomials u(n,x):

1

1 + x

1 + 3x + 2x^2

1 + 6x + 6x^2 + 2x^3

1 + 10x + 12x^2 + 10x^3 + 4x^4

MATHEMATICA

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

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

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[%]    (* A208520 *)

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

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

TableForm[cv]

Flatten[%]    (* A208521 *)

CROSSREFS

Cf. A208521.

Sequence in context: A165958 A113655 A177977 * A114155 A192018 A079513

Adjacent sequences:  A208517 A208518 A208519 * A208521 A208522 A208523

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 28 2012

STATUS

approved

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Last modified October 17 12:56 EDT 2019. Contains 328112 sequences. (Running on oeis4.)