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 A060719 a(0) = 1; a(n+1) = a(n) + Sum_{i=0..n} binomial(n,i)*(a(i)+1). 6
 1, 3, 9, 29, 103, 405, 1753, 8279, 42293, 231949, 1357139, 8427193, 55288873, 381798643, 2765917089, 20960284293, 165729739607, 1364153612317, 11665484410113, 103448316470743, 949739632313501, 9013431476894645, 88304011710168691 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Michael De Vlieger, Table of n, a(n) for n = 0..575 A. R. Ashrafi, L. Ghanbari Maman, K. Kavousi, F. Koorepazan Moftakhar, An Algorithm for Constructing All Supercharacter Theories of a Finite Group, arXiv:1911.12232 [math.GR], 2019. FORMULA a(n) = 2*Bell(n+1) - 1. - Vladeta Jovovic, Feb 11 2003 Equals the binomial transform of A186021. Also, a(n) = A186021(n+1) - 1. - Gary W. Adamson May 20 2013 EXAMPLE a(3) = 29 = (30 - 1) = A186021(4) - 1 MAPLE A060719 := proc(n) option remember; local i; if n=0 then 1 else A060719(n-1)+add(binomial(n-1, i)*(A060719(i)+1), i=0..n-1); fi; end; MATHEMATICA Array[2 BellB[# + 1] - 1 &, 23, 0] (* Michael De Vlieger, Feb 12 2020 *) PROG (PARI) vector(26, n, my(m=n-1); 2*sum(k=0, m+1, stirling(m+1, k, 2)) -1 ) \\ G. C. Greubel, Feb 12 2020 (Magma) [2*Bell(n+1) -1: n in [0..25]]; // G. C. Greubel, Feb 12 2020 (Sage) [2*bell_number(n+1)-1 for n in (0..25)] # G. C. Greubel, Feb 12 2020 CROSSREFS Cf. A000110. Cf. A186021. Sequence in context: A148943 A148944 A293070 * A091152 A148945 A177255 Adjacent sequences: A060716 A060717 A060718 * A060720 A060721 A060722 KEYWORD easy,nonn AUTHOR Frank Ellermann, Apr 23 2001 STATUS approved

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Last modified December 7 01:51 EST 2022. Contains 358649 sequences. (Running on oeis4.)