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A208612 Triangle of coefficients of polynomials u(n,x) jointly generated with A208613; see the Formula section. 3
1, 1, 1, 1, 4, 2, 1, 9, 9, 3, 1, 16, 26, 19, 5, 1, 25, 60, 70, 38, 8, 1, 36, 120, 197, 167, 73, 13, 1, 49, 217, 469, 553, 375, 137, 21, 1, 64, 364, 994, 1528, 1427, 803, 252, 34, 1, 81, 576, 1932, 3714, 4476, 3449, 1661, 457, 55, 1, 100, 870, 3510, 8196 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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)=(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

1...1

1...4....2

1...9....9....3

1...16...26...19...5

First five polynomials u(n,x):

1

1 + x

1 + 4x + 2x^2

1 + 9x + 9x^2 + 3x^3

1 + 16x + 26x^2 + 19x^3 + 5x^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. A208613.

Sequence in context: A177347 A101020 A160905 * A183157 A211957 A063983

Adjacent sequences:  A208609 A208610 A208611 * A208613 A208614 A208615

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 01 2012

STATUS

approved

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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)