A362382
Number of nonisomorphic right involutory magmas with n elements.
Original entry on oeis.org
1, 1, 3, 16, 475, 100666, 267954164, 7178089200724, 2878905036230723360, 16030557330452794172050567, 1643024454743084814743097053747492, 3003719433250221394022136941323628209106412, 119909786948816191249293422143299520925389900896422044
Offset: 0
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B(c,k)=sum(j=0, c\2, if(k%2, 1, 2^(c-2*j))*k^j*binomial(c, 2*j)*(2*j)!/(2^j*j!))
K(v)=my(S=Set(v)); prod(i=1, #S, my(k=S[i], c=#select(t->t==k, v)); B(c,k))
R(v,m)=concat(vector(#v,i,my(t=v[i], g=gcd(t,m)); vector(g, i, t/g)))
a(n)={my(s=0); forpart(p=n, my(v=Vec(p), S=Set(v)); s+=prod(i=1, #S, my(m=S[i], c=#select(t->t==m, v)); (K(R(v,m))/m)^c/c!)); s}
A362643
Number of labeled magmas with n elements satisfying the equations (xy)y = x and x(yz) = xy.
Original entry on oeis.org
1, 1, 2, 10, 94, 1636, 49636, 2489824, 204626528, 27296455456, 5930440245856, 2144594499551296, 1333437360189448768, 1510196144261999035648, 3333925936841219018864384, 15357830414682103475484461056, 155003843551785210349182746546176
Offset: 0
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B(n, k)=my(p=serlaplace(exp(x + x^2/2 + O(x*x^n)))); sum(j=0, n, polcoef(p,j)^k*x^j/j!, O(x*x^n))
seq(n)=Vec(serlaplace(sum(k=0, n, log(B(n-k+1, k))^k/k!)))
A362823
Number of labeled magmas with n elements satisfying the identities (xy)y = x and (xy)z = (xz)y.
Original entry on oeis.org
1, 1, 4, 22, 976, 19376, 7680016, 430723168, 1489656111616, 214815786486400, 6364561150037368576, 2241692646969785651456, 566719960584895502028138496, 471612192582034433034750951424, 1008512943343839231897776246546624512, 1936475539456937172034340659334701398016
Offset: 0
Showing 1-3 of 3 results.
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