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A112519 Riordan array (1,xc(x)*c(-xc(x))), c(x) the g.f. of A000108. 3
1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, 4, 0, 1, 0, 12, 2, 6, 0, 1, 0, 14, 28, 3, 8, 0, 1, 0, 100, 32, 48, 4, 10, 0, 1, 0, 180, 249, 54, 72, 5, 12, 0, 1, 0, 990, 440, 455, 80, 100, 6, 14, 0, 1, 0, 2310, 2552, 792, 726, 110, 132, 7, 16, 0, 1, 0, 10920, 5876, 4836, 1248, 1070, 144, 168, 8, 18, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are A112520. Second column is essentially A055392. Inverse is A112517. Riordan array product (1,xc(x))*(1,xc(-x)).

LINKS

Table of n, a(n) for n=0..77.

FORMULA

Riordan array (1, (sqrt(3-2*sqrt(1-4x))-1)/2); Number triangle T(0, 0)=1, T(n, k)=sum{j=0..n, (k/n)(-1)^(j-k)C(2n-j-1, n-j)C(2j-k-1, j-k)}.

EXAMPLE

Triangle begins

.1;

.0,1;

.0,0,1;

.0,2,0,1;

.0,1,4,0,1;

.0,12,2,6,0,1;

MATHEMATICA

c[x_] := (1 - Sqrt[1 - 4 x])/(2 x);

(* The function RiordanArray is defined in A256893. *)

RiordanArray[1&, # c[#] c[-# c[#]]&, 12] // Flatten (* Jean-Fran├žois Alcover, Jul 16 2019 *)

CROSSREFS

Sequence in context: A185370 A066745 A112517 * A276981 A230305 A091728

Adjacent sequences:  A112516 A112517 A112518 * A112520 A112521 A112522

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Sep 09 2005

STATUS

approved

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Last modified June 22 21:25 EDT 2021. Contains 345392 sequences. (Running on oeis4.)