|
%I #47 Sep 08 2022 08:45:02
%S 1,4,14,51,202,876,4139,21146,115974,678569,4213596,27644436,
%T 190899321,1382958544,10480142146,82864869803,682076806158,
%U 5832742205056,51724158235371,474869816156750,4506715738447322,44152005855084345
%N a(n) = B(n) - 1, where B(n) = Bell numbers, A000110.
%H Vincenzo Librandi, <a href="/A058692/b058692.txt">Table of n, a(n) for n = 2..200</a>
%H W. M. B. Dukes, <a href="http://www.stp.dias.ie/~dukes/matroid.html">Tables of matroids</a>.
%H W. M. B. Dukes, <a href="https://web.archive.org/web/20030208144026/http://www.stp.dias.ie/~dukes/phd.html">Counting and Probability in Matroid Theory</a>, Ph.D. Thesis, Trinity College, Dublin, 2000.
%H W. M. B. Dukes, <a href="https://arxiv.org/abs/math/0411557">On the number of matroids on a finite set</a>, arXiv:math/0411557 [math.CO], 2004.
%H <a href="/index/Mat#matroid">Index entries for sequences related to matroids</a>
%F G.f.: Sum_{k > 1} x^k / ((1 - x) * (1 - x^2) * ... * (1 - x^k)). - _Michael Somos_, Feb 26 2014
%F E.g.f.: exp(exp(x) - 1) - exp(x). - _Ilya Gutkovskiy_, Feb 08 2020
%e G.f. = x^2 + 4*x^3 + 14*x^4 + 51*x^5 + 202*x^6 + 876*x^7 + 4139*x^8 + ...
%t Table[BellB[n, 1] - 1, {n, 2, 23}] (* _Zerinvary Lajos_, Jul 16 2009 *)
%o (Magma) [Bell(n)-1: n in [2..30]]; // _Vincenzo Librandi_, Mar 04 2014
%Y Column k=2 of both A058710 and A058711 (which are the same except for column k=0).
%Y Cf. A000110.
%K nonn
%O 2,2
%A _N. J. A. Sloane_, Dec 30 2000
|
