A362382 Number of nonisomorphic right involutory magmas with n elements.

1, 1, 3, 16, 475, 100666, 267954164, 7178089200724, 2878905036230723360, 16030557330452794172050567, 1643024454743084814743097053747492, 3003719433250221394022136941323628209106412, 119909786948816191249293422143299520925389900896422044

Offset: 0

Author

Andrew Howroyd, Apr 17 2023

Keywords

• nonn

Comments

A magma with element set X is right involutory if (xy)y = x for x,y in X.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..40

Crossrefs

Cf. A001329 (magmas), A076017, A076019, A361720, A362383 (labeled).

Programs

PARI

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}