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A090601 Number of n-element groupoids with an identity. 2
1, 2, 45, 43968, 6358196250, 236919104155855296, 3682959509036574988532481464, 35398008251644050232134479709365068115968, 292415292106611727928759157427747328169866020125762652311 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..9.

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

Eric Weisstein's World of Mathematics, Groupoid.

Index entries for sequences related to groupoids

FORMULA

a(n+1) = 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} ( (1 + sum {d|lcm(i, j)} (d*s_d))^(gcd(i, j)*s_i*s_j))

a(n) asymptotic to n^((n-1)^2+1)/n! = A090602(n)/A000142(n) = A090603(n)/A000142(n-1)

CROSSREFS

Sequence in context: A209606 A100101 A332244 * A266016 A071777 A179108

Adjacent sequences: A090598 A090599 A090600 * A090602 A090603 A090604

KEYWORD

nonn

AUTHOR

Christian G. Bower, Dec 05 2003

STATUS

approved

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Last modified December 2 18:40 EST 2022. Contains 358510 sequences. (Running on oeis4.)