0,3

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Satoh, S.; Yama, K.; and Tokizawa, M., Semigroups of order 8, Semigroup Forum 49 (1994), 7-29. [Background]

T. Tamura, Some contributions of computation to semigroups and groupoids, pp. 229-261 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.

Eric Postpischil Posting to sci.math newsgroup, May 21 1990

Index entries for sequences related to groupoids

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, ...] = prod {i>=j>=1} f(i, j, s_i, s_j) where f(i, j, s_i, s_j) = {i=j, odd} (sum {d|i} (d*s_d))^((i*s_i^2+s_i)/2) or {i=j, even} (sum {d|i} (d*s_d))^(i*s_i^2/2) * (sum {d|i/2} (d*s_d))^s_i or {i != j} (sum {d|lcm(i, j)} (d*s_d))^(2*gcd(i, j)*s_i*s_j)

a(n) asymptotic to (n^binomial(n+1, 2))/n! = A023813(n)/A000142(n) ~ e^n*n^binomial(n, 2) / sqrt(2*pi*n).

a(n)+A079183(n)=A001329(n)

Cf. A001329, A023813, A038016.

Sequence in context: A057134 A041495 A117897 this_sequence A050284 A096759 A006103

Adjacent sequences: A001422 A001423 A001424 this_sequence A001426 A001427 A001428

nonn

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Christian G. Bower (bowerc(AT)usa.net) Feb 15 1998 and May 15 1998. Formula Dec 03 2003.