A002825 Number of precomplete Post functions.

1, 2, 9, 40, 355, 11490, 7758205, 549758283980, 10626621620680257450759, 1701411834605079120446041612344662275078, 79607061350691085453966118726400345961810854094316840855510985234351715774913

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian) Dokl. Akad. Nauk SSSR 186 1969 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..14
• Ivo Rosenberg, The number of maximal closed classes in the set of functions over a finite domain, J. Combinatorial Theory Ser. A 14 (1973), 1-7.
• Ivo Rosenberg and N. J. A. Sloane, Correspondence, 1971
• Zhi-Hong Sun, Congruences for Apéry-like numbers, arXiv:1803.10051 [math.NT], 2018.
• E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian), Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622. [Annotated scanned copy]

Programs

Mathematica

a[1] = 1; a[n_] := -n-2+(-1)^(n-1) Sum[(-1)^k Binomial[n, k] Sum[2^Binomial[ k, j], {j, 0, k}], {k, 0, n-1}];
Array[a, 11] (* Jean-François Alcover, Aug 19 2018 *)

PARI

a(n) = if (n==1, 1, -n - 2 + (-1)^(n-1) * sum(k=0, n-1, (-1)^k * binomial(n, k) * sum(j=0, k, (2^binomial(k, j))))); \\ Michel Marcus, Aug 25 2014

Formula

a(1) = 1. a(n) = -n - 2 + (-1)^(n-1) * Sum_{k=0..n-1} ((-1)^k * binomial(n, k) * Sum_{j=0..k} 2^binomial(k, j)), n > 1. - Sean A. Irvine, Aug 24 2014

Extensions

More terms from Sean A. Irvine, Aug 24 2014