Search: id:A001330
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%I A001330 M5398 N2346
%S A001330 1,1,136,64573605,768614338015543296,740148683083442627372862307855625,
%T A001330 147760220727384062234340471228346859265417269763446784,
%U A001330 13097167596472133103922286145973062271265962292695709182416029922453889335720758
%N A001330 Number of n-element algebras with 2 binary operations.
%C A001330 Isomorphisms classes of a set A with two functions f1,f2: A X A -> A.
%D A001330 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001330 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001330 M. A. Harrison, The number of isomorphism types of finite algebras, Proc. 
               Amer. Math. Soc., 17 (1966), 731-737.
%F A001330 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)).
%F A001330 a(n) is asymptotic to n^(2*n^2)/n! = A008972(n)/A000142(n).
%Y A001330 Cf. A001329, A001331.
%Y A001330 Sequence in context: A071231 A035819 A157880 this_sequence A091510 A134885 
               A082726
%Y A001330 Adjacent sequences: A001327 A001328 A001329 this_sequence A001331 A001332 
               A001333
%K A001330 nonn
%O A001330 0,3
%A A001330 N. J. A. Sloane (njas(AT)research.att.com).
%E A001330 Edited and extended with formula by Christian G. Bower (bowerc(AT)usa.net), 
               Jan 06 2004

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