A006334 - OEIS

%I M2179 #32 Aug 02 2024 22:38:39

%S 0,2,110,2002,20020,136136,705432,2984520,10786908,34370050,98768670,

%T 260390130,638110200,1468635168,3200871520,6650874912,13248113736,

%U 25415833170,47143878782,84832157410,148507792972,253549890440,423093671000,691331713800,1107985378500

%N From the enumeration of corners.

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

%H T. D. Noe, <a href="/A006334/b006334.txt">Table of n, a(n) for n = 0..1000</a>

%H G. Kreweras, <a href="http://www.numdam.org/numdam-bin/item?id=BURO_1965__6__9_0">Sur une classe de problèmes de dénombrement liés au treillis des partitions des entiers</a>, Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique, Université de Paris, 6 (1965), circa p. 82.

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

%F 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.

%F 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

%t 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 *)

%t 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 *)

%Y A row of A132339.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_