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A058692 a(n) = B(n) - 1, where B(n) = Bell numbers, A000110.

%I A058692 #55 May 25 2025 15:20:08
%S A058692 1,4,14,51,202,876,4139,21146,115974,678569,4213596,27644436,
%T A058692 190899321,1382958544,10480142146,82864869803,682076806158,
%U A058692 5832742205056,51724158235371,474869816156750,4506715738447322,44152005855084345
%N A058692 a(n) = B(n) - 1, where B(n) = Bell numbers, A000110.
%H A058692 Vincenzo Librandi, <a href="/A058692/b058692.txt">Table of n, a(n) for n = 2..200</a>
%H A058692 W. M. B. Dukes, <a href="http://www.stp.dias.ie/~dukes/matroid.html">Tables of matroids</a>.
%H A058692 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 A058692 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 A058692 <a href="/index/Mat#matroid">Index entries for sequences related to matroids</a>
%F A058692 G.f.: Sum_{k > 1} x^k / ((1 - x) * (1 - x^2) * ... * (1 - x^k)). - _Michael Somos_, Feb 26 2014
%F A058692 E.g.f.: exp(exp(x) - 1) - exp(x). - _Ilya Gutkovskiy_, Feb 08 2020
%e A058692 G.f. = x^2 + 4*x^3 + 14*x^4 + 51*x^5 + 202*x^6 + 876*x^7 + 4139*x^8 + ...
%p A058692 A058692 := proc(n)
%p A058692     combinat[bell](n)-1 ;
%p A058692 end proc:
%p A058692 seq(A058692(n),n=2..40) ; # _R. J. Mathar_, May 25 2025
%t A058692 Table[BellB[n, 1] - 1, {n, 2, 23}] (* _Zerinvary Lajos_, Jul 16 2009 *)
%o A058692 (Magma) [Bell(n)-1: n in [2..30]]; // _Vincenzo Librandi_, Mar 04 2014
%Y A058692 Column k=2 of both A058710 and A058711 (which are the same except for column k=0).
%Y A058692 Cf. A000110.
%K A058692 nonn
%O A058692 2,2
%A A058692 _N. J. A. Sloane_, Dec 30 2000