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A208524 Triangle of coefficients of polynomials u(n,x) jointly generated with A208525; see the Formula section. 3
1, 1, 1, 1, 3, 3, 1, 6, 10, 5, 1, 10, 22, 23, 11, 1, 15, 40, 65, 60, 21, 1, 21, 65, 145, 195, 137, 43, 1, 28, 98, 280, 490, 518, 322, 85, 1, 36, 140, 490, 1050, 1484, 1372, 723, 171, 1, 45, 192, 798, 2016, 3570, 4368, 3447, 1624, 341, 1, 55, 255, 1230, 3570 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

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

LINKS

Table of n, a(n) for n=1..60.

FORMULA

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

v(n,x)=2x*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

1...3....3

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

1...10...22...23...11

First five polynomials u(n,x):

1

1 + x

1 + 3x + 3x^2

1 + 6x + 10x^2 + 5x^3

1 + 10x + 22x^2 + 23x^3 + 11x^4

MATHEMATICA

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

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

v[n_, x_] := 2 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[%]  (* A208524 *)

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

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

TableForm[cv]

Flatten[%]  (* A208525 *)

Table[u[n, x] /. x -> 1, {n, 1, z}] (*A060816*)

Table[v[n, x] /. x -> 1, {n, 1, z}] (*|A084244|*)

Table[u[n, x] /. x -> -1, {n, 1, z}](*alt. row sums*)

Table[v[n, x] /. x -> -1, {n, 1, z}](*alt. row sums*)

CROSSREFS

Cf. A208525.

Sequence in context: A110640 A143389 A219218 * A094040 A039798 A193560

Adjacent sequences:  A208521 A208522 A208523 * A208525 A208526 A208527

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 29 2012

STATUS

approved

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Last modified October 15 19:25 EDT 2019. Contains 328037 sequences. (Running on oeis4.)