# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a059301 Showing 1-1 of 1 %I A059301 #17 Nov 27 2017 07:40:18 %S A059301 1,5,31,569,165211,12885396101,64563604303081738807, %T A059301 1361129467683753854111752846879267953905, %U A059301 521064401567922879406069432539095585345840013599959430520674634220747299433267 %N A059301 Number of filter bases of an n-set. %D A059301 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 91, #42. %H A059301 Harry J. Smith, Table of n, a(n) for n = 1..12 %F A059301 a(n) = Sum_{k=0..n-1} binomial(n,k)*2^(2^k-1). %F A059301 a(n) ~ n * 2^(2^(n-1)-1). - _Vaclav Kotesovec_, Nov 27 2017 %t A059301 Table[Sum[Binomial[n, k]*2^(2^k - 1), {k, 0, n - 1}], {n, 1, 10}] (* _G. C. Greubel_, Jan 06 2017 *) %o A059301 (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 A059301 (PARI) a(n) = sum(k=0, n-1, binomial(n,k)*2^(2^k-1)); \\ _Michel Marcus_, Jan 03 2016 %K A059301 nonn,easy %O A059301 1,2 %A A059301 _N. J. A. Sloane_, Jan 26 2001 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE