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

0, 0, 1, 10, 105, 1326, 20503, 384126, 8567730, 223587231, 6725042325, 230228283165, 8877197732406, 382107434701266, 18221275474580181, 956287167902779240, 54916689705422813731, 3433293323775503064306, 232614384749689991763561, 17010440815323680947084096

Offset: 0

Author

N. J. A. Sloane, Aug 26 2011

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300
• 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

Crossrefs

Row sums of A193297.

Programs

Magma

[Binomial(Bell(n),2): n in [0..20]]; // Vincenzo Librandi, Feb 17 2018

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 *)

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