OFFSET
1,2
COMMENTS
Partial sums of the number of generalized weak orders on n points. Equivalently, partial sums of the number of bipartitional relations on a set of cardinality n.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..390
FORMULA
a(n) = Sum_{i=1..n} A004123(i).
a(n) = Sum_{i=1..n} Sum_{k >= 0} (k^n*(2/3)^k)/3.
a(n) = Sum_{i=1..n} Sum_{k = 0..n} Stirling2(n,k)*(2^k)*k!.
MATHEMATICA
PROG
(Sage)
def A004123(n): return sum(stirling_number2(n-1, k)*(2^k)*factorial(k) for k in (0..n-1))
[A174278(n) for n in (1..30)] # G. C. Greubel, Mar 25 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 15 2010
STATUS
approved