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a(n) = Catalan(n-1)*Bell(n).
4

%I #25 Oct 15 2024 15:42:58

%S 1,2,10,75,728,8526,115764,1776060,30240210,563870450,11397261720,

%T 247700513242,5750374629244,141819106313800,3698639651089800,

%U 101603353693132215,2929908721122796680,88427704298354261610,2785943404258558905900,91410200883108291556680,3117102657076175159955420

%N a(n) = Catalan(n-1)*Bell(n).

%H Michael De Vlieger, <a href="/A289679/b289679.txt">Table of n, a(n) for n = 1..446</a>

%H Pierre Lescanne, <a href="https://arxiv.org/abs/2104.06723">Zaionc paradox revisited</a>, arXiv:2104.06723 [cs.LO], 2021.

%H Paul Tarau, <a href="https://arxiv.org/abs/1608.03912">A Hiking Trip Through the Orders of Magnitude: Deriving Efficient Generators for Closed Simply-Typed Lambda Terms and Normal Forms</a>, arXiv preprint arXiv:1608.03912 [cs.PL], 2016. See Example 5.

%H Paul Tarau and Valeria de Paiva, <a href="https://vcvpaiva.github.io/includes/pubs/2020-tarau.pdf">Deriving Theorems in Implicational Linear Logic, Declaratively</a>, (2020).

%t Array[CatalanNumber[# - 1] BellB[#] &, 21] (* _Michael De Vlieger_, Aug 04 2017 *)

%o (Python)

%o from sympy.functions.combinatorial.numbers import bell, catalan

%o def A289679(n): return catalan(n-1)*bell(n) # _Chai Wah Wu_, Oct 15 2024

%Y Cf. A000108, A000110, A064299, A289680.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Aug 04 2017