|
Search: id:A001330
|
|
|
| A001330 |
|
Number of n-element algebras with 2 binary operations.
(Formerly M5398 N2346)
|
|
+0
1
|
|
| 1, 1, 136, 64573605, 768614338015543296, 740148683083442627372862307855625, 147760220727384062234340471228346859265417269763446784, 13097167596472133103922286145973062271265962292695709182416029922453889335720758
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Isomorphisms classes of a set A with two functions f1,f2: A X A -> A.
|
|
REFERENCES
|
M. A. Harrison, The number of isomorphism types of finite algebras, Proc. Amer. Math. Soc., 17 (1966), 731-737.
|
|
FORMULA
|
a(n) = sum {1*s_1+2*s_2+...=n} (fix A[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...)) where fix A[s_1, s_2, ...] = Product_{i, j>=1} ( (sum {d|lcm(i, j)} (d*s_d))^(gcd(i, j)*s_i*s_j*2)).
a(n) is asymptotic to n^(2*n^2)/n! = A008972(n)/A000142(n).
|
|
CROSSREFS
|
Cf. A001329, A001331.
Sequence in context: A072897 A071231 A035819 this_sequence A091510 A134885 A082726
Adjacent sequences: A001327 A001328 A001329 this_sequence A001331 A001332 A001333
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
Edited and extended with formula by Christian G. Bower (bowerc(AT)usa.net), Jan 06 2004
|
|
|
Search completed in 0.002 seconds
|
