OFFSET
0,3
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
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
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 *)
PROG
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Andrew Howroyd, Apr 17 2023
STATUS
approved