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A208606 Triangle of coefficients of polynomials u(n,x) jointly generated with A208607; see the Formula section. 3
1, 1, 1, 1, 4, 1, 1, 9, 4, 1, 1, 16, 12, 7, 1, 1, 25, 30, 26, 7, 1, 1, 36, 65, 73, 32, 10, 1, 1, 49, 126, 175, 113, 52, 10, 1, 1, 64, 224, 378, 332, 199, 61, 13, 1, 1, 81, 372, 756, 852, 634, 277, 87, 13, 1, 1, 100, 585, 1422, 1974, 1779, 1024, 421, 99, 16, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..68.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...1

1...4....1

1...9....4....1

1...16...12...7...1

First five polynomials u(n,x):

1

1 + x

1 + 4x + 1x^2

1 + 9x + 4x^2 + x^3

1 + 16x + 12x^2 + 7x^3 + x^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_] := (x + 1)*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[%]  (* A208606 *)

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

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

TableForm[cv]

Flatten[%]  (* A208607 *)

CROSSREFS

Cf. A208607.

Sequence in context: A232530 A231987 A235214 * A136100 A244811 A183153

Adjacent sequences:  A208603 A208604 A208605 * A208607 A208608 A208609

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 29 2012

STATUS

approved

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Last modified October 14 02:29 EDT 2019. Contains 327995 sequences. (Running on oeis4.)