A006334 From the enumeration of corners. (Formerly M2179)

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

0,2

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).

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

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 *)

Crossrefs

A row of A132339.

Sequence in context: A323250 A077804 A063668 * A093425 A091508 A075399

Adjacent sequences: A006331 A006332 A006333 * A006335 A006336 A006337

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved