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A208522 Triangle of coefficients of polynomials u(n,x) jointly generated with A208522; see the Formula section. 3
1, 1, 1, 1, 2, 3, 1, 3, 6, 5, 1, 4, 9, 12, 11, 1, 5, 12, 21, 30, 21, 1, 6, 15, 32, 57, 64, 43, 1, 7, 18, 45, 92, 133, 146, 85, 1, 8, 21, 60, 135, 232, 329, 316, 171, 1, 9, 24, 77, 186, 365, 612, 765, 694, 341, 1, 10, 27, 96, 245, 536, 1015, 1512, 1801, 1496, 683 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..66.

FORMULA

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

v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,

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

EXAMPLE

First five rows:

1

1...1

1...2...3

1...3...6...5

1...4...9...12...11

First five polynomials u(n,x):

1

1 + x

1 + 2x + 3x^2

1 + 3x + 6x^2 + 5x^3

1 + 4x + 9x^2 + 12x^3 + 11x^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_] := 2 x*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[%]    (* A208522 *)

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

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

TableForm[cv]

Flatten[%]    (* A208523 *)

CROSSREFS

Cf. A208523.

Sequence in context: A117938 A256193 A101912 * A209569 A176850 A208516

Adjacent sequences:  A208519 A208520 A208521 * A208523 A208524 A208525

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 29 2012

STATUS

approved

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Last modified October 22 10:20 EDT 2019. Contains 328317 sequences. (Running on oeis4.)