|
|
A367850
|
|
Total sum of the block maxima minus the block minima over all partitions of [n].
|
|
2
|
|
|
0, 0, 1, 6, 33, 182, 1034, 6122, 37927, 246030, 1669941, 11844324, 87644672, 675494180, 5413500801, 45040155758, 388441330457, 3467619369538, 31998729152474, 304846692965822, 2994781617653439, 30304301968015582, 315536869771786501, 3377398077726963112
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: (z-2)*exp(2*z+exp(z)-1)+(2*z+1)*exp(z+exp(z)-1)+exp(exp(z)-1).
a(n) = Bell(n+1)+(n+1)*Bell(n)-Bell(n+2)+Sum_{k=0..n} Stirling2(n+1,k)*(n+1-k).
|
|
EXAMPLE
|
a(3) = 6 = 2 + 1 + 2 + 1 + 0: 123, 12|3, 13|2, 1|23, 1|2|3.
|
|
MAPLE
|
b:= proc(n, m, t) option remember; `if`(n=0, [1, 0], (p->
p+[0, p[1]*(n-t)])(b(n-1, m+1, t+1))+m*b(n-1, m, t+1))
end:
a:= n-> b(n, 0, 1)[2]:
seq(a(n), n=0..23);
# second Maple program:
egf:= (z-2)*exp(2*z+exp(z)-1)+(2*z+1)*exp(z+exp(z)-1)+exp(exp(z)-1):
a:= n-> n!*coeff(series(egf, z, n+1), z, n):
seq(a(n), n=0..23);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|