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URL: https://oeis.org/A060719

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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
OFFSET
0,2
LINKS
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
(SageMath) [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
KEYWORD
easy,nonn
AUTHOR
Frank Ellermann, Apr 23 2001
STATUS
approved