

A090601


Number of nelement groupoids with an identity.


2



1, 2, 45, 43968, 6358196250, 236919104155855296, 3682959509036574988532481464, 35398008251644050232134479709365068115968, 292415292106611727928759157427747328169866020125762652311
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OFFSET

1,2


COMMENTS

Also partial groupoids with n1 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 {dlcm(i, j)} (d*s_d))^(gcd(i, j)*s_i*s_j))
a(n) asymptotic to n^((n1)^2+1)/n! = A090602(n)/A000142(n) = A090603(n)/A000142(n1)


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



