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A209747 Triangle of coefficients of polynomials u(n,x) jointly generated with A209748; see the Formula section. 3
1, 1, 2, 3, 4, 2, 5, 10, 6, 2, 9, 20, 18, 8, 2, 15, 40, 44, 28, 10, 2, 25, 76, 102, 80, 40, 12, 2, 41, 142, 222, 210, 130, 54, 14, 2, 67, 260, 466, 512, 380, 196, 70, 16, 2, 109, 470, 948, 1188, 1022, 630, 280, 88, 18, 2, 177, 840, 1884, 2648, 2590, 1848, 980 (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..62.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...2

3...4....2

5...10...6....2

9...20...18...8...2

First three polynomials u(n,x): 1, 1 + 2x, 3 + 4x + 2x^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] + 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[%]    (* A209747 *)

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

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

TableForm[cv]

Flatten[%]    (* A209748 *)

CROSSREFS

Cf. A209748, A208510.

Sequence in context: A293450 A322990 A120636 * A117744 A091732 A299439

Adjacent sequences:  A209744 A209745 A209746 * A209748 A209749 A209750

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 13 2012

STATUS

approved

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Last modified October 23 05:56 EDT 2019. Contains 328335 sequences. (Running on oeis4.)