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A209555 Triangle of coefficients of polynomials u(n,x) jointly generated with A209556; see the Formula section. 3
1, 1, 1, 2, 2, 1, 2, 5, 3, 1, 3, 6, 9, 4, 1, 3, 11, 13, 14, 5, 1, 4, 12, 28, 24, 20, 6, 1, 4, 19, 34, 59, 40, 27, 7, 1, 5, 20, 62, 80, 110, 62, 35, 8, 1, 5, 29, 70, 164, 166, 188, 91, 44, 9, 1, 6, 30, 115, 200, 376, 314, 301, 128, 54, 10, 1, 6, 41, 125, 365, 496, 776 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

LINKS

Table of n, a(n) for n=1..72.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...1

2...2...1

2...5...3...1

3...6...9...4...1

First three polynomials v(n,x): 1, 1 + x, 2 + 2x + 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];

v[n_, x_] := u[n - 1, x] + 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[%]    (* A209555 *)

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

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

TableForm[cv]

Flatten[%]    (* A209556 *)

CROSSREFS

Cf. A209556, A208510.

Sequence in context: A172021 A325182 A215959 * A059594 A183760 A125678

Adjacent sequences:  A209552 A209553 A209554 * A209556 A209557 A209558

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 10 2012

STATUS

approved

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Last modified October 19 21:28 EDT 2019. Contains 328244 sequences. (Running on oeis4.)