



1, 2, 8, 38, 192, 1002, 5336, 28814, 157184, 864146, 4780008, 26572086, 148321344, 830764794, 4666890936, 26283115038, 148348809216, 838944980514, 4752575891144, 26964373486406, 153196621856192
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Coefficient of x^n in ((1+x)/(1x))^n.  Paul Barry, Jan 20 2008
a(n) is also the number of orderpreserving partial transformations (of an nelement chain). Equivalently, it is the order of the semigroup (monoid) of orderpreserving partial transformations (of an nelement chain), PO sub n.  Abdullahi Umar, Aug 25 2008
Hankel transform is A180966.  Paul Barry, Sep 29 2010


LINKS

Table of n, a(n) for n=0..20.
A. Laradji and A. Umar, A. Combinatorial results for semigroups of orderpreserving partial transformations, Journal of Algebra 278, (2004), 342359.
A. Laradji, and A. Umar, Combinatorial results for semigroups of orderdecreasing partial transformations, J. Integer Seq. 7 (2004), 04.3.8
A. Laradji and A. Umar, Asymptotic results for semigroups of orderpreserving partial transformations Comm. Algebra 34 (2006), 10711075. [From Abdullahi Umar, Oct 11 2008]


FORMULA

a(n)=A122542(2*n,n).  Philippe Deléham, May 28 2007
a(n)=sum{k=0..n, C(n,k)C(n+k1,k)}.  Paul Barry, Aug 22 2007
(2n1)(n+1)a(n+1)= 4(3n^21)a(n)(2n+1)(n1)a(n1), a(0)= 1, a(1)= 2.  Abdullahi Umar, Aug 25 2008
a(n)=Jacobi_P(n,0,1,3).  Paul Barry, Sep 27 2009
G.f.: (1+x+sqrt(16x+x^2))/(2*sqrt(16x+x^2)).  Paul Barry, Sep 29 2010
From Abdullahi Umar, Oct 11 2008: (Start)
a(n+1)  a(n) = (2n+1)A006318 (n>=0);
2*a(n) = (n+1)A006318(n)  (n1)A006318(n1) (n>0). (End)
a(n) = Hyper2F1([n, n], [1], 1).  Peter Luschny, Aug 02 2014


MATHEMATICA

t[n_, m_] = If [n == m == 0, 1, n!*(n + m  1)!/((n  m)!*(n  1)!(m!)^2)]; a = Table[Sum[t[n, m], {m, 0, n}], {n, 0, 20}]; Flatten[a]


CROSSREFS

Essentially identical to A002003.
Sequence in context: A155609 A220542 A199213 * A002003 A059423 A112109
Adjacent sequences: A123161 A123162 A123163 * A123165 A123166 A123167


KEYWORD

nonn


AUTHOR

Roger L. Bagula, Oct 02 2006


EXTENSIONS

Edited by N. J. A. Sloane, Oct 04 2006
Offset changed (a(0)=1) by Michael Somos, Feb 07 2011


STATUS

approved



