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A210200 Triangle of coefficients of polynomials v(n,x) jointly generated with A210199; see the Formula section. 3
1, 2, 2, 4, 5, 2, 7, 12, 7, 2, 12, 25, 21, 9, 2, 20, 50, 53, 32, 11, 2, 33, 96, 124, 94, 45, 13, 2, 54, 180, 273, 250, 150, 60, 15, 2, 88, 331, 577, 617, 445, 223, 77, 17, 2, 143, 600, 1181, 1444, 1212, 728, 315, 96, 19, 2, 232, 1075, 2358, 3242, 3101, 2163 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...

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

LINKS

Table of n, a(n) for n=1..61.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2....2

4....5....2

7....12...7....2

12...25...21...9...2

First three polynomials v(n,x): 1, 2 + 2x , 4 + 5x + 2x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%]   (* A210199 *)

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

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

TableForm[cv]

Flatten[%]   (* A210200 *)

CROSSREFS

Cf. A210199, A208510.

Sequence in context: A109295 A211188 A057899 * A119989 A137605 A242348

Adjacent sequences:  A210197 A210198 A210199 * A210201 A210202 A210203

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 18 2012

STATUS

approved

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Last modified October 19 03:24 EDT 2019. Contains 328211 sequences. (Running on oeis4.)