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A079200 Number of isomorphism classes of associative non-commutative closed binary operations on a set of order n, listed by class size. 6
0, 0, 2, 0, 2, 0, 4, 6, 2, 0, 0, 4, 5, 0, 46, 73, 2, 0, 0, 0, 4, 0, 0, 8, 0, 2, 36, 0, 43, 2, 473, 1020, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 4, 0, 36, 0, 0, 0, 0, 86, 0, 0, 38, 415, 0, 758, 32, 6682, 18426, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Number of elements per row: 1,1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..217 (rows 0..8)
FORMULA
A079194(n,k) + A079197(n,k) + T(n,k) + A079201(n,k) = A079171(n,k).
A079198(n) = Sum_{k>=1} T(n,k)*A079210(n,k).
T(n,k) = A079175(n,k) - A079201(n,k). - Andrew Howroyd, Jan 26 2022
EXAMPLE
Triangle T(n,k) begins:
0;
0;
2, 0;
2, 0, 4, 6;
2, 0, 0, 4, 5, 0, 46, 73;
2, 0, 0, 0, 4, 0, 0, 8, 0, 2, 36, 0, 43, 2, 473, 1020;
...
CROSSREFS
Row sums give A079199.
Sequence in context: A288182 A072680 A067770 * A011420 A035686 A308214
KEYWORD
nonn,tabf
AUTHOR
Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003
EXTENSIONS
a(0)=0 prepended and terms a(16) and beyond from Andrew Howroyd, Jan 26 2022
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)