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A029850 Number of self-converse groupoids. 3
1, 1, 4, 138, 60160, 453292525, 72471180989664, 298545867396801815077, 37263960166680610905649057368, 161614516495439236943507628117344255307, 27480138271604938271870114918720067827110789528890 (list; graph; refs; listen; history; text; internal format)
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} (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*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: A155207 A201388 A089666 * 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

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Last modified June 23 07:38 EDT 2021. Contains 345395 sequences. (Running on oeis4.)