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

KEYWORD

nonn,easy,nice

AUTHOR

EXTENSIONS

Formula and more terms from Christian G. Bower, May 08 1998, Dec 03 2003

STATUS

approved