0,3

Related to partially ordered sets. - Detlef Pauly (dettodet(AT)yahoo.de), Sep 25 2003

The number of partial permutation matrices P in GL_n with P^2=0. Alternatively, the number of orbits of the Borel group of upper triangular matrices acting by conjugation on the set of matrices M in GL_n with M^2=0. - Brian Rothbach (rothbach(AT)math.berkeley.edu), Apr 16 2004

Number of ways to use the elements of {1,..,n} once each to form a collection of sequences, each having length 1 or 2. - Bob Proctor, Apr 18 2005

Hankel transform is A108400. - Paul Barry (pbarry(AT)wit.ie), Feb 11 2008

This is also the number of subsets of equivalent ways to arrange the elements of n pairs, when equivalence is defined under the joint operation of (optional) reversal of elements combined with permutation of the labels and the subset maps to itself. - Ross Drewe (rd(AT)labyrinth.net.au), Mar 16 2008

Equals inverse binomial transform of A000898 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 06 2008]

A. Khruzin, Enumeration of chord diagrams

Index entries for related partition-counting sequences

Index entries for sequences related to Hermite polynomials

seq( sum('n!/((n-2*k)!*k!)', 'k'=0..floor(n/2)), n=0..30 ); - Detlef Pauly (dettodet(AT)yahoo.de), Nov 15 2001

E.g.f.: exp(x^2+x). - Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 11 2001

Binomial transform of A001813 (with interpolated zeros). - Paul Barry (pbarry(AT)wit.ie), May 09 2003

a(n)=sum{k=0..n, C(k,n-k)*n!/k!}; - Paul Barry (pbarry(AT)wit.ie), Mar 29 2007

a(n)=sum{k=0..floor(n/2), C(n,2k)(2k)!/k!}; - Paul Barry (pbarry(AT)wit.ie), Feb 11 2008

G.f.: 1/(1-x-2*x^2/(1-x-4*x^2/(1-x-6*x^2/(1-x-8*x^2/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Apr 10 2009]

with(combstruct):seq(count(([S, {S=Set(Union(Z, Prod(Z, Z)))}, labeled], size=n)), n=0..30); # Detlef Pauly (dettodet(AT)yahoo.de), Sep 25 2003

Range[0, 23]!*CoefficientList[ Series[ Exp[x*(1-x^2)/(1 - x)], {x, 0, 23 }], x] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 23 2007

(MATLAB) N = 18; A = zeros(N, 1); for n = 1:N; a = factorial(n); s = 0; k = 0; while k <= floor(n/2); b = factorial(n - 2*k); c = factorial(k); s = s + a/(b*c); k = k+1; end; A(n) = s; end; disp(A); - Ross Drewe (rd(AT)labyrinth.net.au), Mar 16 2008

Row sums of A067147.

Cf. A000680, A001147, A132101.

A000898 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 06 2008]

Sequence in context: A148734 A124425 A118398 this_sequence A148735 A148736 A148737

Adjacent sequences: A047971 A047972 A047973 this_sequence A047975 A047976 A047977

nonn

N. J. A. Sloane (njas(AT)research.att.com).