login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

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.

Index entries for sequences related to groupoids

FORMULA

F[ n ]=n(1)*prod{i, j >= 1}(sum{d|[ i, j ]}(d*n(d))^((i, j)*n(i)*n(j)))

a(n) = sum {1*s_1+2*s_2+...=n} (fix A[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s2!*...)) where fix A[s_1, s_2, ...] = s_1 * prod {i, j>=1} ( (sum {d|lcm(i, j)} (d*s_d))^(gcd(i, j)*s_i*s_j))

a(n) 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 22 06:24 EST 2019. Contains 320389 sequences. (Running on oeis4.)