A000268 E.g.f.: -log(1+log(1+log(1-x))). (Formerly M3003 N1218)

1, 3, 15, 105, 947, 10472, 137337, 2085605, 36017472, 697407850, 14969626900, 352877606716, 9064191508018, 252024567201300, 7542036496650006, 241721880399970938, 8261159383595659128, 299916384730043070880, 11526945327529620432872, 467583770376898192016104

Offset

1,2

References

J. Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Seiichi Manyama, Table of n, a(n) for n = 1..400 (terms 1..100 from T. D. Noe)

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

Jekuthiel Ginsburg, Iterated exponentials, Scripta Math., 11 (1945), 340-353. [Annotated scanned copy]

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 299

Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565 [math.CO], 2010.

Formula

a(n) = sum((m-1)!*(-1)^(n+m)*sum(stirling1(n, k)*stirling1(k, m), k,m,n), m,1,n), n>0. - Vladimir Kruchinin, Sep 14 2010

Mathematica

max = 20; CoefficientList[-Log[1 + Log[1 + Log[1 - x]]]/x + O[x]^max, x] * Range[max]! (* Jean-François Alcover, Feb 06 2016 *)

Prog

(PARI) a(n) = sum(m=1, n, (m-1)!*(-1)^(n+m)*sum(k=m, n, stirling(n, k, 1)*stirling(k, m, 1))); \\ Michel Marcus, Feb 06 2016

Crossrefs

a(n)=|A039815(n, 1)| (first column of triangle).

Cf. A003713, A000310, A000359, A000406, A001765.

Sequence in context: A001147 A330797 A360438 * A207818 A354218 A118750

Adjacent sequences: A000265 A000266 A000267 * A000269 A000270 A000271

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Revised description from Christian G. Bower, Aug 15 1998

Status

approved