OFFSET
0,4
COMMENTS
Sum of the first entries in all blocks of all set partitions of [n-1]. a(4) = 17 because the sum of the first entries in all blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 1+4+3+3+6 = 17. - Alois P. Heinz, Apr 24 2017
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..400
FORMULA
a(n) = B(n+1)-B(n)-n*B(n-1), where B(q) are the Bell numbers (A000110).
E.g.f.: (exp(z)-1-z)*exp(exp(z)-1).
a(n) = Sum_{k=0..floor(n/2)} k*A124324(n,k).
a(n) = A285595(n-1,1). - Alois P. Heinz, Apr 24 2017
a(n) = Sum_{k=1..n*(n-1)/2} k * A124327(n-1,k) for n>1. - Alois P. Heinz, Dec 05 2023
EXAMPLE
a(3) = 4 because in the partitions 123, 12|3, 13|2, 1|23, 1|2|3 we have four blocks of size >1.
MAPLE
with(combinat): c:=n->bell(n+1)-bell(n)-n*bell(n-1): seq(c(n), n=0..23);
MATHEMATICA
nn=22; Range[0, nn]!CoefficientList[Series[(Exp[x]-1-x)Exp[Exp[x]-1], {x, 0, nn}], x] (* Geoffrey Critzer, Mar 28 2013 *)
PROG
(PARI)
N = 66; x = 'x + O('x^N);
egf = (exp(x)-1-x)*exp(exp(x)-1) + 'c0;
gf = serlaplace(egf);
v = Vec(gf); v[1]-='c0; v
/* Joerg Arndt, Mar 29 2013 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Oct 28 2006
STATUS
approved