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A269796 a(n) = 4^n * A000108(n+1). 1
1, 8, 80, 896, 10752, 135168, 1757184, 23429120, 318636032, 4402970624, 61641588736, 872465563648, 12463793766400, 179478630236160, 2602440138424320, 37965009078190080, 556820133146787840, 8205770383215820800, 121445401671594147840, 1804331681977970196480, 26900945076762464747520 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Samuele Giraudo, Pluriassociative algebras II: The polydendriform operad and related operads, arXiv:1603.01394 [math.CO], 2016. Cf. 2.1.10.

FORMULA

G.f.: (1 - sqrt(1 - 16*x) - 8*x)/(32*x^2). - Bruno Berselli, Mar 07 2016

a(n) = -2^(4*n + 3)*binomial(n + 1/2, -3/2), after Peter Luschny in A000108. - Bruno Berselli, Mar 07 2016

MATHEMATICA

Table[4^n CatalanNumber[n + 1], {n, 0, 20}] (* Bruno Berselli, Mar 07 2016 *)

PROG

(PARI) cat(n) = binomial(2*n, n)/(n+1);

a(n) = 4^n*cat(n+1);

(Sage) [4^n*catalan_number(n+1) for n in (0..20)] # Bruno Berselli, Mar 07 2016

(MAGMA) [4^n*Catalan(n+1): n in [0..25]]; // Vincenzo Librandi, Apr 25 2016

CROSSREFS

Cf. A000108, A003645, A101600.

Sequence in context: A102592 A320759 A233123 * A328128 A053175 A051580

Adjacent sequences:  A269793 A269794 A269795 * A269797 A269798 A269799

KEYWORD

nonn

AUTHOR

Michel Marcus, Mar 07 2016

STATUS

approved

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Last modified July 12 04:30 EDT 2020. Contains 335658 sequences. (Running on oeis4.)