A002825 Number of precomplete Post functions. (Formerly M1935 N0765)

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

Offset

1,2

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]

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A213095 A238372 A308475 * A259339 A346841 A052322

Adjacent sequences: A002822 A002823 A002824 * A002826 A002827 A002828

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Aug 24 2014

Status

approved