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A208607 Triangle of coefficients of polynomials v(n,x) jointly generated with A208606; see the Formula section. 3
1, 3, 1, 5, 3, 1, 7, 8, 6, 1, 9, 18, 19, 6, 1, 11, 35, 47, 25, 9, 1, 13, 61, 102, 81, 42, 9, 1, 15, 98, 203, 219, 147, 51, 12, 1, 17, 148, 378, 520, 435, 216, 74, 12, 1, 19, 213, 666, 1122, 1145, 747, 334, 86, 15, 1, 21, 295, 1119, 2250, 2753, 2233, 1245, 450 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating rows sums: 1,2,3,4,5,6,7,8,...

LINKS

Table of n, a(n) for n=1..63.

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

3...1

5...3...1

7...8...6...1

9...18...19...6...1

First five polynomials v(n,x):

1

3 + x

5 + 3x + x^2

7 + 8x + 6x^2 + x^3

9 + 18x + 19x^2 + 6x^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. A208606.

Sequence in context: A258207 A133094 A300437 * A159291 A122510 A102662

Adjacent sequences:  A208604 A208605 A208606 * A208608 A208609 A208610

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 29 2012

STATUS

approved

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Last modified October 15 12:23 EDT 2019. Contains 328026 sequences. (Running on oeis4.)