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%I
%S 3,12,50,210,882,3696,15444,64350,267410,1108536,4585308,18929092,
%T 78004500,320932800,1318498920,5409723510,22169259090,90751353000,
%U 371125269900,1516311817020,6189965556060,25249187564640
%N Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions.
%C The sequence 1,3,12,50,... is ((n+2)/2)C(2n,n) with g.f. F(1/2,3;2;4x). [From _Paul Barry_, Sep 18 2008]
%D J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 13).
%H J. Propp, <a href="http://www.math.wisc.edu/~propp/articles.html">Publications and Preprints</a>
%H J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), <a href="http://www.msri.org/publications/books/Book38/contents.html">New Perspectives in Algebraic Combinatorics</a>
%F a(n) = (2*n-1)!/((n-1)!)^2+(2*n)!/(n!)^2; A056347(n) = A002457(n-1) + A000984(n).
%F a(n) = (n+2)*A001700(n-1). - _Vladeta Jovovic_, Jul 12 2004
%F n*a(n) +(-7*n+4)*a(n-1) +6*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Nov 30 2012
%e a(3)=5!/2!2!+6!/3!3!=50.
%o (Mupad) combinat::catalan(n) *binomial(n+2,2) $ n = 1..22 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 15 2007
%Y Cf. A000984, A002457.
%Y Cf. A092437-A092442.
%K easy,nonn,changed
%O 1,1
%A Christopher Hanusa (chanusa(AT)math.washington.edu), Mar 24 2004
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