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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 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 STATUS approved

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