|
| |
|
|
A075900
|
|
G.f.: Product_{n>0} 1/(1 - 2^(n-1)*x^n).
|
|
3
| |
|
|
1, 1, 3, 7, 19, 43, 115, 259, 659, 1523, 3731, 8531, 20883, 47379, 113043, 259219, 609683, 1385363, 3245459, 7344531, 17028499, 38579603, 88585619, 199845267, 457864595, 1028904339, 2339763603, 5256820115, 11896157587, 26626389395
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
LINKS
| N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
|
|
|
FORMULA
| a(n) = Sum_{ partitions n = c_1 + ... + c_k } 2^(n-k). If p(n, m) = number of partitions of n into m parts, a(n) = sum_{m=1..n} p(n, m)*2^(n-m).
Sum_{n>=0} (a(n)/2^n)*x^n = Product_{n>0} 1/(1-x^n/2); a(n) = 1/n*Sum_{k=1..n} A080267(k)*a(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 11 2003
|
|
|
MAPLE
| oo := 101; t1 := mul(1/(1-x^n/2), n=1..oo): t2 := series(t1, x, oo-1): t3 := seriestolist(t2): A075900 := n->2^n*t3[n+1];
with(combinat); A075900 := proc(n) local i, t1, t2, t3; t1 := partition(n); t2 := 0; for i from 1 to nops(t1) do t3 := t1[i]; t2 := t2+2^(n-nops(t3)); od: t2; end;
|
|
|
CROSSREFS
| Sequence in context: A127990 A192301 A055622 * A176500 A069051 A136041
Adjacent sequences: A075897 A075898 A075899 * A075901 A075902 A075903
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Oct 15 2002
|
|
|
EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 11 2003
|
| |
|
|
