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%I M1935 N0765 #39 Sep 30 2023 13:07:55
%S 1,2,9,40,355,11490,7758205,549758283980,10626621620680257450759,
%T 1701411834605079120446041612344662275078,
%U 79607061350691085453966118726400345961810854094316840855510985234351715774913
%N Number of precomplete Post functions.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D 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.
%H Alois P. Heinz, <a href="/A002825/b002825.txt">Table of n, a(n) for n = 1..14</a>
%H Ivo Rosenberg, <a href="http://dx.doi.org/10.1016/0097-3165(73)90058-7">The number of maximal closed classes in the set of functions over a finite domain</a>, J. Combinatorial Theory Ser. A 14 (1973), 1-7.
%H Ivo Rosenberg and N. J. A. Sloane, <a href="/A002824/a002824_1.pdf">Correspondence, 1971</a>
%H Zhi-Hong Sun, <a href="https://arxiv.org/abs/1803.10051">Congruences for Apéry-like numbers</a>, arXiv:1803.10051 [math.NT], 2018.
%H E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, <a href="/A002824/a002824.pdf">Precomplete classes in k-valued logics. (Russian)</a>, Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622. [Annotated scanned copy]
%F 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
%t 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}];
%t Array[a, 11] (* _Jean-François Alcover_, Aug 19 2018 *)
%o (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
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Aug 24 2014