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A209581 Triangle of coefficients of polynomials u(n,x) jointly generated with A209582; see the Formula section. 3
1, 1, 1, 2, 4, 1, 2, 8, 11, 1, 3, 12, 25, 26, 1, 3, 19, 51, 71, 57, 1, 4, 24, 88, 180, 190, 120, 1, 4, 34, 136, 348, 566, 486, 247, 1, 5, 40, 206, 628, 1238, 1648, 1199, 502, 1, 5, 53, 282, 1034, 2526, 4070, 4545, 2873, 1013, 1, 6, 60, 395, 1600, 4556, 9208 (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..61.

FORMULA

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

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

1...1

2...4....1

2...8....11...1

3...12...25...26...1

First three polynomials v(n,x): 1, 1 + x, 2 + 4x + 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_] := (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[%]   (* A209581 *)

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

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

TableForm[cv]

Flatten[%]   (* A209582 *)

CROSSREFS

Cf. A209582, A208510.

Sequence in context: A194671 A131398 A249307 * A050980 A053451 A254076

Adjacent sequences:  A209578 A209579 A209580 * A209582 A209583 A209584

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 11 2012

STATUS

approved

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Last modified August 18 13:25 EDT 2019. Contains 326100 sequences. (Running on oeis4.)