A193274 - OEIS

%I #45 Sep 08 2022 08:45:58

%S 0,0,1,10,105,1326,20503,384126,8567730,223587231,6725042325,

%T 230228283165,8877197732406,382107434701266,18221275474580181,

%U 956287167902779240,54916689705422813731,3433293323775503064306,232614384749689991763561,17010440815323680947084096

%N a(n) = binomial(Bell(n), 2) where B(n) = Bell numbers A000110(n).

%H Alois P. Heinz, <a href="/A193274/b193274.txt">Table of n, a(n) for n = 0..300</a>

%H Frank Ruskey and Jennifer Woodcock, <a href="http://dx.doi.org/10.1007/978-3-642-25011-8_23">The Rand and block distances of pairs of set partitions</a>, in International Workshop on Combinatorial Algorithms, Victoria, 2011. LNCS.

%H Frank Ruskey, Jennifer Woodcock and Yuji Yamauchi, <a href="http://dx.doi.org/10.1016/j.jda.2012.04.003">Counting and computing the Rand and block distances of pairs of set partitions</a>, Journal of Discrete Algorithms, Volume 16, October 2012, Pages 236-248. - From _N. J. A. Sloane_, Oct 03 2012

%p a:= n-> binomial(combinat[bell](n), 2):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Aug 28 2011

%t a[n_] := With[{b = BellB[n]}, b*(b-1)/2]; Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Mar 18 2014 *)

%o (Magma) [Binomial(Bell(n),2): n in [0..20]]; // _Vincenzo Librandi_, Feb 17 2018

%o (Python)

%o from itertools import accumulate, islice

%o def A193274_gen(): # generator of terms

%o     yield 0

%o     blist, b = (1,), 1

%o     while True:

%o         blist = list(accumulate(blist, initial=(b:=blist[-1])))

%o         yield b*(b-1)//2

%o A193274_list = list(islice(A193274_gen(),30)) # _Chai Wah Wu_, Jun 22 2022

%Y Row sums of A193297.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Aug 26 2011