

A007160


Number of diagonal dissections of a convex (n+6)gon into n regions.
(Formerly M5094)


5



1, 20, 225, 1925, 14014, 91728, 556920, 3197700, 17587350, 93486536, 483367885, 2442687975, 12109051500, 59053512000, 283963030560, 1348824395160, 6338392712550, 29503515951000, 136173391604250
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OFFSET

1,2


COMMENTS

Number of standard tableaux of shape (n,n,1,1,1,1) (see Stanley reference).  Emeric Deutsch, May 20 2004
Number of increasing tableaux of shape (n+4,n+4) with largest entry 2n+4. An increasing tableau is a semistandard tableau with strictly increasing rows and columns, such that the set of entries forms an initial segment of the positive integers.  Oliver Pechenik, May 02 2014
a(n) = number of noncrossing partitions of 2n+4 into n blocks all of size at least 2.  Oliver Pechenik, May 02 2014


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS



FORMULA

Dfinite with recurrence (n+5)(n1)*n*a(n) = 2(2n+3)(n+3)(n+2)a(n1).
a(n) = binomial(n+3, 4)*binomial(2n+4, n1)/n.


MATHEMATICA

a[n_] := (n+1)(n+2)(n+3)*Binomial[2n+4, n1]/24; Table[a[n], {n, 1, 19}](* JeanFrançois Alcover, Nov 16 2011 *)


PROG

(Magma) [Binomial(n+3, 4)*Binomial(2*n+4, n1)/n : n in [1..30]]; // Vincenzo Librandi, Nov 17 2011


CROSSREFS



KEYWORD

easy,nonn,nice


AUTHOR



EXTENSIONS

Offset is correct!


STATUS

approved



