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A209753 Triangle of coefficients of polynomials u(n,x) jointly generated with A209754; see the Formula section. 3
1, 1, 2, 3, 5, 3, 5, 14, 12, 4, 9, 30, 40, 23, 5, 15, 63, 107, 93, 39, 6, 25, 124, 264, 300, 190, 61, 7, 41, 238, 604, 858, 722, 354, 90, 8, 67, 445, 1319, 2242, 2364, 1559, 615, 127, 9, 109, 818, 2772, 5500, 6966, 5783, 3101, 1011, 173, 10, 177, 1482 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...

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

LINKS

Table of n, a(n) for n=1..57.

FORMULA

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

v(n,x)=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...2

3...5....3

5...14...12...4

9...30...40...23...5

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

MATHEMATICA

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

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

v[n_, x_] := 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[%]    (* A209753 *)

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

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

TableForm[cv]

Flatten[%]    (* A209754 *)

CROSSREFS

Cf. A209754, A208510.

Sequence in context: A193957 A209769 A114230 * A185191 A103781 A095244

Adjacent sequences:  A209750 A209751 A209752 * A209754 A209755 A209756

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 14 2012

STATUS

approved

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Last modified October 16 03:28 EDT 2019. Contains 328040 sequences. (Running on oeis4.)