A362821 Number of labeled right involutory Płonka magmas with n elements.

1, 1, 2, 10, 70, 916, 16636, 494824, 20486432, 1320568624, 119526633136, 16466317431136, 3210471529800448, 940911157770908416, 392559353168479443584, 244017910517578226511616, 216775189886094655708439296, 284778404550532041821957456896, 536018349047631899870416803595264

Offset: 0

Author

Andrew Howroyd, May 08 2023

Keywords

• nonn

Comments

A right involutory Płonka magma is a magma satisfying the identities (xy)y = x, (xy)z = (xz)y and x(yz) = xy. See A361720 for additional information.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A361720 (isomorphism classes), A362643, A362822, A362824.

Programs

PARI

\\ 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!)))

Formula

E.g.f.: Sum_{k>=0} log(B(k,x))^k/k! where B(k,x) is the e.g.f. of column k of A362824.