OFFSET
0,3
COMMENTS
Two involutions x,y on [n] commute if x*y = y*x (i.e. x(y(i)) = y(x(i)) for i in [n]).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
FORMULA
PROG
(PARI) b(n, f) = {sum(k=0, n\2, f(k)*binomial(n, 2*k)*(2*k)!/(k!*2^k))}
a(n) = {b(n, k->b(n-2*k, j->1)*b(k, j->2^(k-j)))}
(PARI) seq(n)=Vec(serlaplace(exp(x + 3*x^2/2 + x^4/4 + O(x*x^n))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, May 05 2023
STATUS
approved