The first 47 terms of A001168, from Don Knuth Jan 9, 2001 Dear Neil, I've got further news re sequence A001168: My old program POLYENUM is now obsoleted by a new program POLYNUM, which implements Jensen's algorithm with a few refinements. The URL is still the same as before. With the new program I extended the enumeration to n=47, and verified all of Jensen's results thru n=46. Since his algorithm is nontrivial, I was expecting in fact that our results would NOT agree; many possibilities for subtle errors exist, including errors that would not show up for small n. Thus the fact that we got identical values is reasonably convincing that the numbers are correct. And here are those numbers: 1 2 6 19 63 216 760 2725 9910 36446 135268 505861 1903890 7204874 27394666 104592937 400795844 1540820542 5940738676 22964779660 88983512783 345532572678 1344372335524 5239988770268 20457802016011 79992676367108 313224032098244 1228088671826973 4820975409710116 18946775782611174 74541651404935148 293560133910477776 1157186142148293638 4565553929115769162 18027932215016128134 71242712815411950635 281746550485032531911 1115021869572604692100 4415695134978868448596 17498111172838312982542 69381900728932743048483 275265412856343074274146 1092687308874612006972082 4339784013643393384603906 17244800728846724289191074 68557762666345165410168738 272680844424943840614538634 The program is a fairly good test of memory --- it needs something like 850 MB of RAM and about 10 GB of disk --- and takes about a week to run. I ran it twice, on two different machines. (Actually on five different machines, three of which proved to be flaky! That's what I meant about it being a fairly good test of memory.) Depending on how long Moore's law holds up, we can expect slightly more than one new value per year (always computed in a week, of course), for the next ten years. After that my data structure will need 24 bytes per node instead of 20.... Don