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A207629 Triangle of coefficients of polynomials u(n,x) jointly generated with A207630; see the Formula section. 4
1, 2, 5, 1, 11, 4, 23, 13, 1, 47, 37, 6, 95, 97, 25, 1, 191, 241, 87, 8, 383, 577, 271, 41, 1, 767, 1345, 783, 169, 10, 1535, 3073, 2143, 609, 61, 1, 3071, 6913, 5631, 2001, 291, 12, 6143, 15361, 14335, 6145, 1191, 85, 1, 12287, 33793, 35583, 17921 (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 - 3*z + 2*z^2), z^2/(1 - 2*z)) in the notation of Corsani et al., Section 2. - Peter Bala, Dec 31 2015

LINKS

Table of n, a(n) for n=1..53.

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

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

EXAMPLE

First five rows:

   1

   2

   5  1

  11  4

  23 13  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 + 1)*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[%]    (* A207629 *)

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

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

TableForm[cv]

Flatten[%]    (* A207630 *)

CROSSREFS

Cf. A207630, A208510, A083329 (column 1).

Sequence in context: A120235 A323411 A089618 * A207614 A156067 A263487

Adjacent sequences:  A207626 A207627 A207628 * A207630 A207631 A207632

KEYWORD

nonn,tabf,easy

AUTHOR

Clark Kimberling, Feb 23 2012

STATUS

approved

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Last modified June 26 04:11 EDT 2019. Contains 324369 sequences. (Running on oeis4.)