A006334 From the enumeration of corners.

0, 2, 110, 2002, 20020, 136136, 705432, 2984520, 10786908, 34370050, 98768670, 260390130, 638110200, 1468635168, 3200871520, 6650874912, 13248113736, 25415833170, 47143878782, 84832157410, 148507792972, 253549890440, 423093671000, 691331713800, 1107985378500

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

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

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• G. Kreweras, Sur une classe de problèmes de dénombrement liés au treillis des partitions des entiers, Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique, Université de Paris, 6 (1965), circa p. 82.
• Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Crossrefs

A row of A132339.

Programs

Mathematica

Abs@ With[{n = 5}, Table[(2 (-1)^(n + k) (n + k - 1)! (2 n + 2 k - 3)!)/(n! k! (2 n - 1)! (2 k - 1)!), {k, 0, 24}]] (* Michael De Vlieger, Mar 26 2016 *)
LinearRecurrence[{13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1},{0,2,110,2002,20020,136136,705432,2984520,10786908,34370050,98768670,260390130,638110200},30] (* Harvey P. Dale, Apr 21 2016 *)

Formula

a(n) = (n*(1 + n)^2*(2 + n)^2*(3 + n)^2*(4 + n)*(1 + 2*n)*(3 + 2*n)*(5 + 2*n)*(7 + 2*n))/1360800.

G.f.: -2*x*(x+1)*(x^6 + 41*x^5 + 323*x^4 + 678*x^3 + 323*x^2 + 41*x + 1)/(x-1)^13. - Colin Barker, Sep 19 2012