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A208613 Triangle of coefficients of polynomials v(n,x) jointly generated with A208612; see the Formula section. 3
1, 3, 2, 5, 7, 3, 7, 17, 16, 5, 9, 34, 51, 33, 8, 11, 60, 127, 129, 65, 13, 13, 97, 272, 386, 302, 124, 21, 15, 147, 525, 975, 1052, 666, 231, 34, 17, 212, 938, 2186, 3049, 2646, 1409, 423, 55, 19, 294, 1578, 4482, 7757, 8650, 6285, 2887, 764, 89, 21 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..56.

FORMULA

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

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

3...2

5...7....3

7...17...16...3

9...34...51...33...8

First five polynomials v(n,x):

1

3 + 2x

5 + 7x + 3x^2

7 + 17x + 16x^2 + 3x^3

9 + 34x + 51x^2 + 33x^3 + 8x^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] + (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[%]  (* A208612 *)

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

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

TableForm[cv]

Flatten[%]  (* A208613 *)

CROSSREFS

Cf. A208612.

Sequence in context: A128224 A125026 A130295 * A209584 A209140 A265903

Adjacent sequences:  A208610 A208611 A208612 * A208614 A208615 A208616

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 01 2012

STATUS

approved

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Last modified October 19 16:08 EDT 2019. Contains 328223 sequences. (Running on oeis4.)