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A208525 Triangle of coefficients of polynomials v(n,x) jointly generated with A208524; see the Formula section. 3
1, 2, 3, 3, 7, 5, 4, 12, 18, 11, 5, 18, 42, 49, 21, 6, 25, 80, 135, 116, 43, 7, 33, 135, 295, 381, 279, 85, 8, 42, 210, 560, 966, 1050, 638, 171, 9, 52, 308, 966, 2086, 2996, 2724, 1453, 341, 10, 63, 432, 1554, 4032, 7182, 8688, 6921, 3240, 683, 11, 75 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

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

2...3

3...7....5

4...12...18...11

5...18...42...49...21

First five polynomials v(n,x):

1

2 + 3x

3 + 7x + 5x^2

4 + 12x + 18x^2 + 11x^3

5 + 18x + 42x^2 + 49x^3 + 21x^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. A208524.

Sequence in context: A168140 A088100 A097359 * A209574 A079387 A141061

Adjacent sequences:  A208522 A208523 A208524 * A208526 A208527 A208528

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 29 2012

STATUS

approved

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Last modified February 18 05:37 EST 2019. Contains 320245 sequences. (Running on oeis4.)