A029850 Number of self-converse groupoids.

1, 1, 4, 138, 60160, 453292525, 72471180989664, 298545867396801815077, 37263960166680610905649057368, 161614516495439236943507628117344255307, 27480138271604938271870114918720067827110789528890

Offset

0,3

Links

Table of n, a(n) for n=0..10.

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} (sum {d|i*2} (d*s_d))^((i*s_i^2-s_i)/2) * (sum {d|i} (d*s_d))^s_i or {i=j == 0 mod 4} (sum {d|i} (d*s_d))^(i*s_i^2) or {i=j == 2 mod 4} (sum {d|i} (d*s_d))^(i*s_i^2-s_i) * (sum {d|i/2} (d*s_d))^(2*s_i) or {i != j} (sum {d|lcm(i, j, 2)} (d*s_d))^(2*i*j*s_i*s_j/lcm(2*i*j)).

Crossrefs

a(n) = 2*A001424(n) - A001329(n). Cf. A001425.

Sequence in context: A201388 A089666 A363114 * A221675 A340838 A291450

Adjacent sequences: A029847 A029848 A029849 * A029851 A029852 A029853

Keyword

nonn

Author

Christian G. Bower, Jan 15 1998, Jun 15 1998, Dec 05 2003

Extensions

Formula corrected by Sean A. Irvine and Christian G. Bower, Jul 13 2012

Status

approved