OFFSET
0,4
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * binomial(2*k+1,n-2*k)/( (2*k+1)*k! ).
a(n) ~ n^(n-1) / (sqrt(2) * exp(n) * r^(n+1)), where r = 0.450347181930267755599214125867779338412791581819135528888185619948594... and s = 2.1478259175343697310213089706837271102656629945040966643073615920885... are roots of the system of equations exp(r^2*s^2)*r = s-1, 2*(s-1)*r^2*s = 1. - Vaclav Kotesovec, Mar 10 2024
PROG
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k*binomial(2*k+1, n-2*k)/((2*k+1)*k!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 09 2024
STATUS
approved