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A006332 From the enumeration of corners.
(Formerly M2148)
2
0, 2, 28, 168, 660, 2002, 5096, 11424, 23256, 43890, 77924, 131560, 212940, 332514, 503440, 742016, 1068144, 1505826, 2083692, 2835560, 3801028, 5026098, 6563832, 8475040, 10829000, 13704210, 17189172, 21383208, 26397308, 32355010 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

Table of n, a(n) for n=0..29.

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.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

FORMULA

a(n) = (n*(1 + n)^2*(2 + n)*(1 + 2*n)*(3 + 2*n))/90.

G.f.: 2*(x+1)*(x^2 + 6*x + 1)/(1-x)^7.

MAPLE

A006332:=-2*(1+z)*(z**2+6*z+1)/(z-1)**7; # conjectured by Simon Plouffe in his 1992 dissertation

MATHEMATICA

Table[(n (1 + n)^2 (2 + n) (1 + 2 n) (3 + 2 n))/90, {n, 0, 30}] (* or *)

{0}~Join~CoefficientList[Series[2 (x + 1) (x^2 + 6 x + 1)/(1 - x)^7, {x, 0, 29}], x] (* Michael De Vlieger, Mar 26 2016 *)

PROG

(PARI) x='x+O('x^99); concat(0, Vec(2*(x+1)*(x^2+6*x+1)/(1-x)^7)) \\ Altug Alkan, Mar 26 2016

CROSSREFS

Equals 2*A006858. A row of A132339.

Sequence in context: A164834 A174707 A110241 * A280120 A065340 A001798

Adjacent sequences:  A006329 A006330 A006331 * A006333 A006334 A006335

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 16 04:02 EDT 2018. Contains 316259 sequences. (Running on oeis4.)