A362383 Number of labeled right involutory magmas with n elements.

1, 1, 4, 64, 10000, 11881376, 192699928576, 36175612601171968, 116077185312503648813056, 5817168207073186596352000000000, 5962207128673051739782035558293177368576, 119898867867315010793162270409575082620582830800896, 57436979804085599487337333419576950752550097125586310052970496

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..30

Crossrefs

Cf. A000085, A002489 (magmas), A076016, A362382 (isomorphism classes).

Programs

Maple

b:= proc(n) b(n):= `if`(n<2, 1, b(n-1)+(n-1)*b(n-2)) end:
a:= n-> b(n)^n:
seq(a(n), n=0..15);  # Alois P. Heinz, Apr 30 2023

Mathematica

A85[n_] := Sum[StirlingS1[n, k]*2^k*BellB[k, 1/2], {k, 0, n}];
a[n_] := A85[n]^n;
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Mar 14 2025, after Emanuele Munarini in A85 *)

PARI

\\ here b(n) is A000085(n).
b(n)=sum(j=0, n\2, binomial(n, 2*j)*(2*j)!/(2^j*j!))
a(n)=b(n)^n

Formula

a(n) = A000085(n)^n.

a(n) ~ exp(-7/48 + 7*sqrt(n)/24 - n/4 + n^(3/2) - n^2/2) * n^(n^2/2) / 2^(n/2). - Vaclav Kotesovec, Mar 14 2025