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 A006448 Number of n-element algebras with 1 binary operator and 1 constant (pointed groupoids). (Formerly M5029) 2
 1, 16, 9882, 715860992, 12417636281312500, 85953540009068492207916672, 356838302112667713247240882121025536249, 1245456693529103515171728481423145699858332531028201472 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS M. A. Harrison, The number of isomorphism types of finite algebras, Proc. Amer. Math. Soc., 17 (1966), 731-737. FORMULA For a list n(1), n(2), n(3), ..., let fixF[n] = n(1)*Product_{i, j >= 1} (Sum_{d|[ i, j ]} (d*n(d))^((i, j)*n(i)*n(j))), where [i,j] = lcm(i,j). [Note that the notation fixF[n] appears in several other formulas contributed by Christian G. Bower. In this case it seems that the prefix "fix" was accidentally removed over the course of the years. - N. J. A. Sloane, Dec 19 2021] a(n) = Sum_{1*s_1+2*s_2+...=n} (fixA[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s2!*...)) where fixA[s_1, s_2, ...] = s_1 * Product_{i, j>=1} ( (Sum_{d|lcm(i, j)} (d*s_d))^(gcd(i, j)*s_i*s_j)). a(n) is asymptotic to n^(n^2+1)/n!. CROSSREFS Cf. A001329. Sequence in context: A151641 A265240 A221137 * A017092 A265634 A191945 Adjacent sequences:  A006445 A006446 A006447 * A006449 A006450 A006451 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Formula and more terms from Christian G. Bower, May 08 1998, Dec 03 2003 STATUS approved

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Last modified May 19 12:20 EDT 2022. Contains 353833 sequences. (Running on oeis4.)