A058692 a(n) = B(n) - 1, where B(n) = Bell numbers, A000110.
1, 4, 14, 51, 202, 876, 4139, 21146, 115974, 678569, 4213596, 27644436, 190899321, 1382958544, 10480142146, 82864869803, 682076806158, 5832742205056, 51724158235371, 474869816156750, 4506715738447322, 44152005855084345
Offset: 2
Keywords
Examples
G.f. = x^2 + 4*x^3 + 14*x^4 + 51*x^5 + 202*x^6 + 876*x^7 + 4139*x^8 + ...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 2..200
- W. M. B. Dukes, Tables of matroids.
- W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000.
- W. M. B. Dukes, On the number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004.
- Index entries for sequences related to matroids
Crossrefs
Programs
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Magma
[Bell(n)-1: n in [2..30]]; // Vincenzo Librandi, Mar 04 2014
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Maple
A058692 := proc(n) combinat[bell](n)-1 ; end proc: seq(A058692(n),n=2..40) ; # R. J. Mathar, May 25 2025
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Mathematica
Table[BellB[n, 1] - 1, {n, 2, 23}] (* Zerinvary Lajos, Jul 16 2009 *)
Formula
G.f.: Sum_{k > 1} x^k / ((1 - x) * (1 - x^2) * ... * (1 - x^k)). - Michael Somos, Feb 26 2014
E.g.f.: exp(exp(x) - 1) - exp(x). - Ilya Gutkovskiy, Feb 08 2020