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A208527 Triangle of coefficients of polynomials v(n,x) jointly generated with A208526; see the Formula section. 3
1, 1, 4, 1, 4, 10, 1, 4, 12, 28, 1, 4, 14, 40, 76, 1, 4, 16, 52, 124, 208, 1, 4, 18, 64, 176, 384, 568, 1, 4, 20, 76, 232, 592, 1168, 1552, 1, 4, 22, 88, 292, 832, 1936, 3520, 4240, 1, 4, 24, 100, 356, 1104, 2880, 6240, 10512, 11584, 1, 4, 26, 112, 424, 1408 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..61.

FORMULA

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

v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,

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

EXAMPLE

First five rows:

1

1...4

1...4...10

1...4...12...28

1...4...14...40...76

First five polynomials v(n,x):

1

1 + 4x

1 + 4x + 10x^2

1 + 4x + 12x^2 + 28x^3

1 + 4x + 14x^2 + 40x^3 + 76x^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] + 2 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[%]  (* A208526 *)

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

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

TableForm[cv]

Flatten[%]  (* A208527 *)

CROSSREFS

Cf. A208526.

Sequence in context: A007891 A165487 A201286 * A209576 A055886 A132478

Adjacent sequences:  A208524 A208525 A208526 * A208528 A208529 A208530

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 29 2012

STATUS

approved

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Last modified October 17 16:20 EDT 2019. Contains 328117 sequences. (Running on oeis4.)