%I M5398 N2346 #24 Dec 19 2021 14:00:43
%S 1,1,136,64573605,768614338015543296,
%T 740148683083442627372862307855625,
%U 147760220727384062234340471228346859265417269763446784,13097167596472133103922286145973062271265962292695709182416029922453889335720758
%N Number of n-element algebras with 2 binary operations.
%C Isomorphisms classes of a set A with two functions f1,f2: A X A -> A.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H M. A. Harrison, <a href="https://doi.org/10.1090/S0002-9939-1966-0200219-9">The number of isomorphism types of finite algebras</a>, Proc. Amer. Math. Soc., 17 (1966), 731-737.
%F 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)).
%F a(n) is asymptotic to n^(2*n^2)/n! = A008972(n)/A000142(n).
%Y Cf. A001329, A001331.
%K nonn
%O 0,3
%A _N. J. A. Sloane_
%E Edited and extended with formula by _Christian G. Bower_, Jan 06 2004