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A092443 Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions. 7
3, 12, 50, 210, 882, 3696, 15444, 64350, 267410, 1108536, 4585308, 18929092, 78004500, 320932800, 1318498920, 5409723510, 22169259090, 90751353000, 371125269900, 1516311817020, 6189965556060, 25249187564640 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence 1,3,12,50,... is ((n+2)/2)C(2n,n) with g.f. F(1/2,3;2;4x). - Paul Barry, Sep 18 2008

REFERENCES

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).

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..1659

J. Propp, Publications and Preprints

J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), New Perspectives in Algebraic Combinatorics

FORMULA

a(n) = (2*n-1)!/((n-1)!)^2+(2*n)!/(n!)^2; A056347(n) = A002457(n-1) + A000984(n).

a(n) = (n+2)*A001700(n-1). - Vladeta Jovovic, Jul 12 2004

n*a(n) + (-7*n+4)*a(n-1) + 6*(2*n-3)*a(n-2) = 0. - R. J. Mathar, Nov 30 2012

EXAMPLE

a(3) = 5!/2!2! + 6!/3!3! = 50.

MATHEMATICA

Array[Binomial[2 # + 1, # + 1] &[# - 1]*(# + 2) &, 22] (* Michael De Vlieger, Dec 17 2017 *)

PROG

(MuPAD) combinat::catalan(n) *binomial(n+2, 2) $ n = 1..22 // Zerinvary Lajos, Feb 15 2007

(PARI) a(n) = (n+2)*binomial(2*n-1, n); \\ Altug Alkan, Dec 17 2017

CROSSREFS

Cf. A000984, A002457.

Cf. A092437, A092438, A092439, A092440, A092441, A092442.

Sequence in context: A037765 A037653 A229665 * A108080 A113441 A119976

Adjacent sequences:  A092440 A092441 A092442 * A092444 A092445 A092446

KEYWORD

easy,nonn

AUTHOR

Christopher Hanusa (chanusa(AT)math.washington.edu), Mar 24 2004

STATUS

approved

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Last modified March 24 12:14 EDT 2019. Contains 321448 sequences. (Running on oeis4.)