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A362382 Number of nonisomorphic right involutory magmas with n elements. 7
1, 1, 3, 16, 475, 100666, 267954164, 7178089200724, 2878905036230723360, 16030557330452794172050567, 1643024454743084814743097053747492, 3003719433250221394022136941323628209106412, 119909786948816191249293422143299520925389900896422044 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
A magma with element set X is right involutory if (xy)y = x for x,y in X.
LINKS
PROG
(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}
CROSSREFS
Cf. A001329 (magmas), A076017, A076019, A361720, A362383 (labeled).
Sequence in context: A081782 A176299 A081780 * A297118 A002794 A132559
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Apr 17 2023
STATUS
approved

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Last modified July 12 09:44 EDT 2024. Contains 374239 sequences. (Running on oeis4.)