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