OFFSET
0,3
COMMENTS
Partially ordered sets on n elements that consist entirely of floor(n/2) chains (nonempty, linearly ordered subsets).
FORMULA
a(n) = Sum_{j=floor(n/2)..n} |Stirling1(n, j)|*Stirling2(j, floor(n/2)).
a(n) = binomial(n - 1, floor(n/2) - 1)*n!/floor(n/2)!) for n >= 1, a(0) = 1.
a(n) = A271703(n, floor(n/2)).
MAPLE
a := n -> `if`(n=0, 1, binomial(n - 1, iquo(n, 2) - 1)*n!/iquo(n, 2)!):
seq(a(n), n = 0..21);
PROG
(SageMath)
def a(n): return binomial(n, n - n//2)*falling_factorial(n - 1, n - n//2)
print([a(n) for n in range(22)])
(PARI) a(n) = sum(j=n\2, n, abs(stirling(n, j, 1))*stirling(j, n\2, 2)); \\ Michel Marcus, Apr 22 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Apr 21 2021
STATUS
approved