|
| |
|
|
A102661
|
|
Triangle of partial sums of Stirling numbers of 2nd kind (cf. A048993): T(n,k) = Sum_{i=1..k} Stirling2(n,i), 1<=k<=n.
|
|
3
| |
|
|
1, 1, 2, 1, 4, 5, 1, 8, 14, 15, 1, 16, 41, 51, 52, 1, 32, 122, 187, 202, 203, 1, 64, 365, 715, 855, 876, 877, 1, 128, 1094, 2795, 3845, 4111, 4139, 4140, 1, 256, 3281, 11051, 18002, 20648, 21110, 21146, 21147, 1, 512, 9842, 43947, 86472, 109299, 115179, 115929
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| T(n,k) is the number of ways to place n distinguishable balls into k indistinguishable bins. [Geoffrey Critzer, Mar 22 2011]
|
|
|
REFERENCES
| Richard Stanley, Enumerative Combinatorics, Cambridge Univ. Press, 1997 page 38. (#7 of the twelvefold ways)
|
|
|
EXAMPLE
| Triangle begins:
1;
1,2;
1,4,5;
1,8,14,15;
1,16,41,51,52; ....
|
|
|
MAPLE
| with(combinat): A102661_row := proc(n) local k, j; seq(add(stirling2(n, j), j=1..k), k=1..n) end:
seq(print(A102661_row(r)), r=1..6); # Peter Luschny, Sep. 30 2011
|
|
|
MATHEMATICA
| Table[Table[Sum[StirlingS2[n, i], {i, 1, k}], {k, 1, n}], {n, 1, 10}] // Grid (* Geoffrey Critzer, Mar 22 2011*)
|
|
|
CROSSREFS
| Cf. A008949, A049444.
Sequence in context: A121289 A134248 A080935 * A121574 A117317 A124237
Adjacent sequences: A102658 A102659 A102660 * A102662 A102663 A102664
|
|
|
KEYWORD
| easy,nonn,tabl
|
|
|
AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 03 2005
|
| |
|
|
