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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

Table of n, a(n) for n=1..8.

M. A. Harrison, The number of isomorphism types of finite algebras, Proc. Amer. Math. Soc., 17 (1966), 731-737.

Index entries for sequences related to groupoids

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

N. J. A. Sloane

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.)