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A207616 Triangle of coefficients of polynomials u(n,x) jointly generated with A207617; see the Formula section. 4
1, 2, 4, 1, 7, 4, 11, 11, 1, 16, 25, 6, 22, 50, 22, 1, 29, 91, 63, 8, 37, 154, 154, 37, 1, 46, 246, 336, 129, 10, 56, 375, 672, 375, 56, 1, 67, 550, 1254, 957, 231, 12, 79, 781, 2211, 2211, 781, 79, 1, 92, 1079, 3718, 4719, 2288, 377, 14, 106, 1456, 6006 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

With offset 0, equals the stretched Riordan array ((1 - z + z^2)/(1 - z)^3, z^2/(1 - z)^2) in the notation of Corsani et al., Section 2. - Peter Bala, Dec 31 2015

LINKS

Table of n, a(n) for n=1..59.

C. Corsani, D. Merlini, R. Sprugnoli, Left-inversion of combinatorial sums Discrete Mathematics, 180 (1998) 107-122.

FORMULA

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

   4  1

   7  4

  11 11  1

MATHEMATICA

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

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

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

Table[Factor[u[n, x]], {n, 1, z}]

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

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]    (* A207616 *)

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

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

TableForm[cv]

Flatten[%]    (* A207617 *)

CROSSREFS

Cf. A207617, A208510, A000124 (column 1).

Sequence in context: A119303 A256107 A207610 * A105552 A112852 A121531

Adjacent sequences:  A207613 A207614 A207615 * A207617 A207618 A207619

KEYWORD

nonn,tabf,easy

AUTHOR

Clark Kimberling, Feb 20 2012

STATUS

approved

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Last modified October 14 01:36 EDT 2019. Contains 327994 sequences. (Running on oeis4.)