A006333 From the enumeration of corners. (Formerly M2175)

0, 2, 60, 660, 4290, 20020, 74256, 232560, 639540, 1586310, 3617900, 7696260, 15438150, 29451240, 53796160, 94607040, 160908264, 265670730, 427156860, 670609940, 1030350090, 1552346268, 2297341200, 3344614000, 4796473500

Offset

0,2

References

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

Links

Matthew House, Table of n, a(n) for n = 0..10000

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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(n) = (n*(1 + n)^2*(2 + n)^2*(3 + n)*(1 + 2*n)*(3 + 2*n)*(5 + 2*n))/7560.

G.f.: 2*(1 + 20*x + 75*x^2 + 75*x^3 + 20*x^4 + x^5)/(1-x)^10.

Mathematica

Abs@ With[{n = 4}, Table[(2 (-1)^(n + k) (n + k - 1)! (2 n + 2 k - 3)!)/(n! k! (2 n - 1)! (2 k - 1)!), {k, 0, 24}]] (* or *)
{0}~Join~CoefficientList[Series[2 (1 + 20 x + 75 x^2 + 75 x^3 + 20 x^4 + x^5)/(1 - x)^10, {x, 0, 23}], x] (* Michael De Vlieger, Mar 26 2016 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 2, 60, 660, 4290, 20020, 74256, 232560, 639540, 1586310}, 30] (* Harvey P. Dale, Jan 01 2017 *)

Prog

(PARI) a(n) = (n*(1 + n)^2*(2 + n)^2*(3 + n)*(1 + 2*n)*(3 + 2*n)*(5 + 2*n))/7560 \\ Charles R Greathouse IV, Jul 28 2015
(PARI) x='x+O('x^99); concat(0, Vec(2*(1+20*x+75*x^2+75*x^3+20*x^4+x^5)/(1-x)^10)) \\ Altug Alkan, Mar 26 2016

Crossrefs

A row of A132339.

Sequence in context: A067739 A187626 A059934 * A001760 A230572 A157059

Adjacent sequences: A006330 A006331 A006332 * A006334 A006335 A006336

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved