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Number of labeled right involutory Płonka magmas with n elements.
3

%I #9 May 28 2023 22:21:07

%S 1,1,2,10,70,916,16636,494824,20486432,1320568624,119526633136,

%T 16466317431136,3210471529800448,940911157770908416,

%U 392559353168479443584,244017910517578226511616,216775189886094655708439296,284778404550532041821957456896,536018349047631899870416803595264

%N Number of labeled right involutory Płonka magmas with n elements.

%C 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.

%H Andrew Howroyd, <a href="/A362821/b362821.txt">Table of n, a(n) for n = 0..100</a>

%F 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.

%o (PARI) D(n,k) is e.g.f. of column k of A362824.

%o B(n, k)={polcoef(x^k/prod(j=0, k, 1-2^j*x + O(x*x^n)), n)}

%o D(n, k)=exp(sum(j=0, min(k, logint(n, 2)), B(k, j)*x^(2^j)/2^j, O(x*x^n)))

%o seq(n)=Vec(serlaplace(sum(k=0, n, log(D(n-k+1, k))^k/k!)))

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

%K nonn

%O 0,3

%A _Andrew Howroyd_, May 08 2023