A090604 Number of n-element self-converse groupoids with an identity.

1, 2, 15, 944, 725500, 9319882896, 2537598028922726, 17768840869582166129408, 3754397843576564028373337684409, 27480138271604938576005130925123233245100

Offset

1,2

Comments

Also partial self-converse groupoids with n-1 elements or self-converse groupoids with an absorbant (zero) element with n elements.

Links

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, Groupoid

Index entries for sequences related to groupoids

Formula

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, ...] = prod {i>=j>=1} f(i, j, s_i, s_j) where f(i, j, s_i, s_j) = {i=j, odd} (1 + sum {d|i*2} (d*s_d)) ^ ((i*s_i^2-s_i)/2) * (1 + sum {d|i} (d*s_d))^s_i or {i=j == 0 mod 4} (1 + sum {d|i} (d*s_d))^(i*s_i^2) or {i=j == 2 mod 4} (1 + sum {d|i})^(i*s_i^2-s_i) * (1 + sum {d|i/2} (d*s_d))^(2*s_i) or {i != j} (1 + sum {d|lcm(i, j, 2)} (d*s_d))^(2*gcd(i, j)*s_i*s_j/(s_i*s_j*lcm(2*i*j)))

Crossrefs

Sequence in context: A216331 A179432 A007542 * A007467 A132317 A068409

Adjacent sequences: A090601 A090602 A090603 * A090605 A090606 A090607

Keyword

nonn

Author

Christian G. Bower, Dec 05 2003

Status

approved