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A193274
a(n) = binomial(Bell(n), 2) where B(n) = Bell numbers A000110(n).
3
0, 0, 1, 10, 105, 1326, 20503, 384126, 8567730, 223587231, 6725042325, 230228283165, 8877197732406, 382107434701266, 18221275474580181, 956287167902779240, 54916689705422813731, 3433293323775503064306, 232614384749689991763561, 17010440815323680947084096
OFFSET
0,4
LINKS
Frank Ruskey and Jennifer Woodcock, The Rand and block distances of pairs of set partitions, in International Workshop on Combinatorial Algorithms, Victoria, 2011. LNCS.
Frank Ruskey, Jennifer Woodcock and Yuji Yamauchi, Counting and computing the Rand and block distances of pairs of set partitions, Journal of Discrete Algorithms, Volume 16, October 2012, Pages 236-248. - From N. J. A. Sloane, Oct 03 2012
MAPLE
a:= n-> binomial(combinat[bell](n), 2):
seq(a(n), n=0..20); # Alois P. Heinz, Aug 28 2011
MATHEMATICA
a[n_] := With[{b = BellB[n]}, b*(b-1)/2]; Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Mar 18 2014 *)
PROG
(Magma) [Binomial(Bell(n), 2): n in [0..20]]; // Vincenzo Librandi, Feb 17 2018
(Python)
from itertools import accumulate, islice
def A193274_gen(): # generator of terms
yield 0
blist, b = (1, ), 1
while True:
blist = list(accumulate(blist, initial=(b:=blist[-1])))
yield b*(b-1)//2
A193274_list = list(islice(A193274_gen(), 30)) # Chai Wah Wu, Jun 22 2022
CROSSREFS
Row sums of A193297.
Sequence in context: A000457 A240681 A113348 * A068883 A087599 A337826
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 26 2011
STATUS
approved