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
-
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}
A362385
Number of nonisomorphic magmas with n elements satisfying the equation x(yz) = xy.
Original entry on oeis.org
1, 1, 3, 14, 197, 6139, 603933, 199410617
Offset: 0
A362642
Number of nonisomorphic magmas with n elements satisfying the equations (xy)y = x and x(yz) = xy.
Original entry on oeis.org
1, 1, 2, 4, 13, 47, 255, 1810, 18471, 266931
Offset: 0
A362821
Number of labeled right involutory Płonka magmas with n elements.
Original entry on oeis.org
1, 1, 2, 10, 70, 916, 16636, 494824, 20486432, 1320568624, 119526633136, 16466317431136, 3210471529800448, 940911157770908416, 392559353168479443584, 244017910517578226511616, 216775189886094655708439296, 284778404550532041821957456896, 536018349047631899870416803595264
Offset: 0
-
\\ D(n,k) is e.g.f. of column k of A362824.
B(n, k)={polcoef(x^k/prod(j=0, k, 1-2^j*x + O(x*x^n)), n)}
D(n, k)=exp(sum(j=0, min(k, logint(n, 2)), B(k, j)*x^(2^j)/2^j, O(x*x^n)))
seq(n)=Vec(serlaplace(sum(k=0, n, log(D(n-k+1, k))^k/k!)))
A362822
Number of nonisomorphic magmas with n elements satisfying the identities (xy)y = x and (xy)z = (xz)y.
Original entry on oeis.org
1, 1, 3, 6, 68, 254, 14310, 112762, 43419892
Offset: 0
Showing 1-5 of 5 results.
Comments