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A209583 Triangle of coefficients of polynomials u(n,x) jointly generated with A209584; see the Formula section. 3
1, 1, 1, 3, 3, 1, 5, 10, 6, 1, 9, 23, 24, 10, 1, 15, 51, 71, 49, 15, 1, 25, 104, 188, 178, 90, 21, 1, 41, 205, 452, 552, 390, 153, 28, 1, 67, 391, 1025, 1530, 1396, 776, 245, 36, 1, 109, 730, 2218, 3927, 4394, 3169, 1435, 374, 45, 1, 177, 1339, 4636, 9502 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Alternating row sums: 1,0,1,0,1,0,1,0,1,0,1,0,...

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

LINKS

Table of n, a(n) for n=1..59.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...1

3...3....1

5...10...6....1

9...23...24...10...1

First three polynomials u(n,x): 1, 1 + x, 3 + 3x + 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] + (x + 1)*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[%]   (* A209583 *)

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

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

TableForm[cv]

Flatten[%]   (* A209584 *)

CROSSREFS

Cf. A209584, A208510.

Sequence in context: A208610 A193823 A071945 * A144944 A137426 A269949

Adjacent sequences:  A209580 A209581 A209582 * A209584 A209585 A209586

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 11 2012

STATUS

approved

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)