|
| |
|
|
A053488
|
|
E.g.f.: exp(exp(sinh(x))-1)-1.
|
|
0
|
|
|
|
0, 1, 2, 6, 23, 103, 535, 3153, 20676, 149148, 1172343, 9960085, 90864801, 885278605, 9167936406, 100508961982, 1162366436355, 14136151459043, 180287711599455, 2405321659729837, 33495442060505752, 485880832780748932
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
a(n) is the number of pairs (d,d') of set partitions of {1,2,...,n} such that d is finer than d' and all block sizes of d are odd. - Geoffrey Critzer, Dec 28 2011.
|
|
|
REFERENCES
|
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.1.14.
|
|
|
LINKS
|
Table of n, a(n) for n=0..21.
Vladimir Kruchinin, Compositae and their properties, arXiv:1103.2582~
|
|
|
FORMULA
|
a(n)=sum(m=1..n, sum(1/(2^k*k!)*sum(i=0..k, (-1)^i*binomial(k,i)*(k-2*i)^n)*stirling2(k,m),k,m,n)), n>0. [From Vladimir Kruchinin, Sep 10 2010]
|
|
|
MATHEMATICA
|
nn = 21; a = Sinh[x]; Range[0, nn]! CoefficientList[Series[Exp[Exp[a] - 1] - 1, {x, 0, nn}], x] (*Geoffrey Critzer, Dec 28 2011*)
|
|
|
PROG
|
(Maxima) a(n):=sum(sum(1/(2^k*k!)*sum((-1)^i*binomial(k, i)*(k-2*i)^n, i, 0, k)*stirling2(k, m), k, m, n), m, 1, n); [From Vladimir Kruchinin, Sep 10 2010]
|
|
|
CROSSREFS
|
Sequence in context: A216040 A005802 A061552 * A117106 A137534 A137535
Adjacent sequences: A053485 A053486 A053487 * A053489 A053490 A053491
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane, Jan 15 2000
|
|
|
STATUS
|
approved
|
| |
|
|
