|
| |
|
|
A059098
|
|
Triangle T(n,m)=Sum_{i=0..n} stirling2(n,i)*Product_{j=1..m} (i-j+1), m=0..n.
|
|
1
|
|
|
|
1, 1, 1, 2, 3, 2, 5, 10, 12, 6, 15, 37, 62, 60, 24, 52, 151, 320, 450, 360, 120, 203, 674, 1712, 3120, 3720, 2520, 720, 877, 3263, 9604, 21336, 33600, 34440, 20160, 5040, 4140, 17007, 56674, 147756, 287784, 394800, 352800, 181440, 40320, 21147, 94828
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
COMMENTS
|
T(n,0)=A000110; T(n,1)=A005493. Row sums give A059099.
|
|
|
LINKS
|
Table of n, a(n) for n=0..46.
|
|
|
FORMULA
|
E.g.f. for T(n, m): (exp(x)-1)^m*(exp(exp(x)-1)).
|
|
|
EXAMPLE
|
Triangle begins:
[1],
[1, 1],
[2, 3, 2],
[5, 10, 12, 6],
[15, 37, 62, 60, 24],
[52, 151, 320, 450, 360, 120], ...;
E.g.f. for T(n, 2) = (exp(x)-1)^2*(exp(exp(x)-1)) = x^2 + 2*x^3 + 31/12*x^4 + 8/3*x^5 + 107/45*x^6 + 343/180*x^7 + 28337/20160*x^8 + 349/360*x^9 + ...;
E.g.f. for T(n, 3) = (exp(x)-1)^3*(exp(exp(x)-1)) = x^3 + 5/2*x^4 + 15/4*x^5 + 13/3*x^6 + 127/30*x^7 + 1759/480*x^8 + 34961/12096*x^9 + ...
n-th row is M^n*[1,0,0,0,...], where M is a tridiagonal matrix with all 1's in the superdiagonal, (1,2,3,...) in the main and subdiagonals; and the rest zeros. - Gary W. Adamson, Jun 23 2011
|
|
|
CROSSREFS
|
Cf. A049020, A001861, A059099.
Sequence in context: A079535 A050159 A147294 * A082050 A183098 A183101
Adjacent sequences: A059095 A059096 A059097 * A059099 A059100 A059101
|
|
|
KEYWORD
|
easy,nonn,tabl,changed
|
|
|
AUTHOR
|
Vladeta Jovovic, Jan 02 2001
|
|
|
STATUS
|
approved
|
| |
|
|
