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Number of filter bases of an n-set.
1

%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