%I #17 Nov 27 2017 07:40:18
%S 1,5,31,569,165211,12885396101,64563604303081738807,
%T 1361129467683753854111752846879267953905,
%U 521064401567922879406069432539095585345840013599959430520674634220747299433267
%N Number of filter bases of an n-set.
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 91, #42.
%H Harry J. Smith, <a href="/A059301/b059301.txt">Table of n, a(n) for n = 1..12</a>
%F a(n) = Sum_{k=0..n-1} binomial(n,k)*2^(2^k-1).
%F a(n) ~ n * 2^(2^(n-1)-1). - _Vaclav Kotesovec_, Nov 27 2017
%t Table[Sum[Binomial[n, k]*2^(2^k - 1), {k, 0, n - 1}], {n, 1, 10}] (* _G. C. Greubel_, Jan 06 2017 *)
%o (PARI) { for (n = 1, 12, a=0; for (k=0, n-1, a+=binomial(n, k)*2^(2^k - 1); ); write("b059301.txt", n, " ", a); ) } \\ _Harry J. Smith_, Jun 25 2009
%o (PARI) a(n) = sum(k=0, n-1, binomial(n,k)*2^(2^k-1)); \\ _Michel Marcus_, Jan 03 2016
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Jan 26 2001