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A193274 a(n) = binomial(Bell(n), 2) where B(n) = Bell numbers A000110(n).

%I A193274 #45 Sep 08 2022 08:45:58
%S A193274 0,0,1,10,105,1326,20503,384126,8567730,223587231,6725042325,
%T A193274 230228283165,8877197732406,382107434701266,18221275474580181,
%U A193274 956287167902779240,54916689705422813731,3433293323775503064306,232614384749689991763561,17010440815323680947084096
%N A193274 a(n) = binomial(Bell(n), 2) where B(n) = Bell numbers A000110(n).
%H A193274 Alois P. Heinz, <a href="/A193274/b193274.txt">Table of n, a(n) for n = 0..300</a>
%H A193274 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 A193274 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 A193274 a:= n-> binomial(combinat[bell](n), 2):
%p A193274 seq(a(n), n=0..20);  # _Alois P. Heinz_, Aug 28 2011
%t A193274 a[n_] := With[{b = BellB[n]}, b*(b-1)/2]; Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Mar 18 2014 *)
%o A193274 (Magma) [Binomial(Bell(n),2): n in [0..20]]; // _Vincenzo Librandi_, Feb 17 2018
%o A193274 (Python)
%o A193274 from itertools import accumulate, islice
%o A193274 def A193274_gen(): # generator of terms
%o A193274     yield 0
%o A193274     blist, b = (1,), 1
%o A193274     while True:
%o A193274         blist = list(accumulate(blist, initial=(b:=blist[-1])))
%o A193274         yield b*(b-1)//2
%o A193274 A193274_list = list(islice(A193274_gen(),30)) # _Chai Wah Wu_, Jun 22 2022
%Y A193274 Row sums of A193297.
%K A193274 nonn
%O A193274 0,4
%A A193274 _N. J. A. Sloane_, Aug 26 2011