|
| |
|
|
A007405
|
|
Dowling numbers: binomial transform of A004211.
(Formerly M1674)
|
|
5
| |
|
|
1, 2, 6, 24, 116, 648, 4088, 28640, 219920, 1832224, 16430176, 157554048, 1606879040, 17350255744, 197553645440, 2363935624704, 29638547505408, 388328781668864, 5304452565517824, 75381218537805824
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Equals leftmost term in iterates of M^n * [1,1,1,...], where M = a bidiagonal matrix with (1,3,5,7,...) in the main diagonal and (1,1,1,...) in the superdiagonal. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 13 2009]
|
|
|
REFERENCES
| Benoumhani, Moussa; On Whitney numbers of Dowling lattices. Discrete Math. 159 (1996), no. 1-3, 13-33.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
N. J. A. Sloane, Transforms
|
|
|
FORMULA
| E.g.f.: exp(z + 1/2 exp(2 z) - 1/2).
Row sums of triangles A039755, A039756 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 20 2005
a(n) = sum of top row terms of M^n, M = an infinite square production matrix in which a diagonal of 1's is appended to the right of Pascal's triangle squared; as follows:
1, 1, 0, 0, 0, 0,...
2, 1, 1, 0, 0, 0,...
4, 4, 1, 1, 0, 0,...
8, 12, 6, 1, 1, 0,...
16, 32, 24, 8, 1, 1,...
... - Gary W. Adamson, Aug 01 2011
|
|
|
EXAMPLE
| a(4) = 116 = sum of top row terms of M^3 = (49 + 44 + 18 + 4 + 1)
|
|
|
MATHEMATICA
| max = 19; f[x_] := Exp[x + Exp[2x]/2 - 1/2]; CoefficientList[ Series[ f[x], {x, 0, max}], x]*Range[0, max]! (* From Jean-François Alcover, Nov 22 2011 *)
|
|
|
CROSSREFS
| Sequence in context: A069657 A082631 A097483 * A177518 A164871 A079106
Adjacent sequences: A007402 A007403 A007404 * A007406 A007407 A007408
|
|
|
KEYWORD
| nonn,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
