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A210194 Triangle of coefficients of polynomials v(n,x) jointly generated with A210193; see the Formula section. 3
1, 2, 3, 3, 11, 3, 4, 26, 20, 3, 5, 50, 74, 29, 3, 6, 85, 204, 149, 38, 3, 7, 133, 469, 547, 251, 47, 3, 8, 196, 952, 1618, 1160, 380, 56, 3, 9, 276, 1764, 4110, 4234, 2124, 536, 65, 3, 10, 375, 3048, 9318, 13036, 9262, 3520, 719, 74, 3, 11, 495, 4983 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..58.

FORMULA

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

v(n,x)=2x*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

2...3

3...11...3

4...26...20...3

5...50...74...29...3

First three polynomials v(n,x): 1, 2 + 3x , 3 + 11x + 3x^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_] := 2 x*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[%]   (* A210193 *)

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

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

TableForm[cv]

Flatten[%]  (* A210194 *)

CROSSREFS

Cf. A210193, A208510.

Sequence in context: A117030 A155758 A009097 * A210755 A219224 A265532

Adjacent sequences:  A210191 A210192 A210193 * A210195 A210196 A210197

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 18 2012

STATUS

approved

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Last modified October 21 03:24 EDT 2019. Contains 328291 sequences. (Running on oeis4.)