A060719 a(0) = 1; a(n+1) = a(n) + Sum_{i=0..n} binomial(n,i)*(a(i)+1).

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

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