A068604 Number of distinct coefficients in expansion related to enumeration of permutations of length n by length of longest subsequence.

1, 1, 2, 3, 6, 9, 16, 29, 51, 84, 138, 227, 370, 603, 980, 1589, 2576, 4172, 6756, 10936, 17700, 28646, 46357, 75013, 121381, 196405

Offset

1,3

Comments

Hammersely has incorrect a(9)=55 in Table XIII on p. 387, due to four errors in Table XIV. In particular, the values 4168, 3772, 1475, and 2203 should be 3751, 3820, 1892, and 2255, respectively. Since these values occur elsewhere in the list, the number of distinct values is reduced to 51. - Sean A. Irvine, Feb 28 2024

References

J. M. Hammersley, A few seedings of research, in Proc. Sixth Berkeley Sympos. Math. Stat. and Prob., ed. L. M. le Cam et al., Univ. Calif. Press, 1972, Vol. I, pp. 345-394.

Links

Table of n, a(n) for n=1..26.

Sean A. Irvine, Java program (github)

Crossrefs

Sequence in context: A017915 A114702 A026768 * A174023 A014868 A029463

Adjacent sequences: A068601 A068602 A068603 * A068605 A068606 A068607

Keyword

nonn,more

Author

N. J. A. Sloane, Mar 29 2002

Extensions

a(9) corrected and a(10)-a(26) from Sean A. Irvine, Feb 28 2024

Status

approved