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

%I A362821 #12 May 08 2025 19:41:11
%S A362821 1,1,2,10,70,916,16636,494824,20486432,1320568624,119526633136,
%T A362821 16466317431136,3210471529800448,940911157770908416,
%U A362821 392559353168479443584,244017910517578226511616,216775189886094655708439296,284778404550532041821957456896,536018349047631899870416803595264
%N A362821 Number of labeled right involutory Płonka magmas with n elements.
%C A362821 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 A362821 Andrew Howroyd, <a href="/A362821/b362821.txt">Table of n, a(n) for n = 0..100</a>
%F A362821 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 A362821 (PARI) \\ D(n,k) is e.g.f. of column k of A362824.
%o A362821 B(n, k)={polcoef(x^k/prod(j=0, k, 1-2^j*x + O(x*x^n)), n)}
%o A362821 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 A362821 seq(n)=Vec(serlaplace(sum(k=0, n, log(D(n-k+1, k))^k/k!)))
%Y A362821 Cf. A361720 (isomorphism classes), A362643, A362822, A362824.
%K A362821 nonn
%O A362821 0,3
%A A362821 _Andrew Howroyd_, May 08 2023