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A209150 Triangle of coefficients of polynomials u(n,x) jointly generated with A208335; see the Formula section. 2
1, 2, 1, 4, 4, 1, 7, 10, 5, 1, 11, 21, 17, 7, 1, 16, 40, 46, 28, 8, 1, 22, 71, 107, 87, 39, 10, 1, 29, 119, 224, 232, 144, 55, 11, 1, 37, 190, 434, 555, 443, 226, 70, 13, 1, 46, 291, 792, 1221, 1198, 773, 328, 91, 14, 1, 56, 430, 1377, 2511, 2942, 2318, 1255 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..62.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...1

4...4.....1

7...10....5....1

11...21...17...7...1

First three polynomials v(n,x): 1, 2 + x, 4 + 4x + x^2.

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];

v[n_, x_] := 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[%]    (* A209150 *)

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

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

TableForm[cv]

Flatten[%]    (* A208335 *)

CROSSREFS

Cf. A208335, A208510.

Sequence in context: A154558 A220836 A008572 * A209145 A214984 A118976

Adjacent sequences:  A209147 A209148 A209149 * A209151 A209152 A209153

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 07 2012

STATUS

approved

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)