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A208509 Triangle of coefficients of polynomials v(n,x) jointly generated with A208508; see the Formula section. 4
1, 3, 5, 1, 7, 5, 9, 14, 1, 11, 30, 7, 13, 55, 27, 1, 15, 91, 77, 9, 17, 140, 182, 44, 1, 19, 204, 378, 156, 11, 21, 285, 714, 450, 65, 1, 23, 385, 1254, 1122, 275, 13, 25, 506, 2079, 2508, 935, 90, 1, 27, 650, 3289, 5148, 2717, 442, 15, 29, 819, 5005, 9867 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

col 1:  A005408

col 2:  A000330 (square pyramidal numbers)

col 3:  A005585

col 4:  A050486

col 5:  A054333

col 6:  A057788

row sums, v(n,1):  A003948

alternating row sums, v(n,-1):  A090131

LINKS

Table of n, a(n) for n=1..60.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

3

5...1

7...5

9...14...1

First five polynomials v(n,x):

1

3

5 + x

7 + 5x

9 + 14x + x^2

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_] := 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[%]    (* A208508 *)

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

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

TableForm[cv]

Flatten[%]    (* A208509 *)

CROSSREFS

Cf. A208508.

Sequence in context: A202356 A152204 A114216 * A086233 A242390 A065395

Adjacent sequences:  A208506 A208507 A208508 * A208510 A208511 A208512

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Feb 27 2012

STATUS

approved

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Last modified September 22 20:55 EDT 2014. Contains 247086 sequences.