A001330 Number of n-element algebras with 2 binary operations. (Formerly M5398 N2346)

1, 1, 136, 64573605, 768614338015543296, 740148683083442627372862307855625, 147760220727384062234340471228346859265417269763446784, 13097167596472133103922286145973062271265962292695709182416029922453889335720758

Offset

0,3

Comments

Isomorphisms classes of a set A with two functions f1,f2: A X A -> A.

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..7.

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} (fixA[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...)) where fixA[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: A233127 A157880 A233254 * A091510 A134885 A259680

Adjacent sequences: A001327 A001328 A001329 * A001331 A001332 A001333

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited and extended with formula by Christian G. Bower, Jan 06 2004

Status

approved