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

0,4

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

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

Adjacent sequences: A193271 A193272 A193273 * A193275 A193276 A193277

Keyword

nonn

Author

N. J. A. Sloane, Aug 26 2011

Status

approved