Search: id:A005584
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%I A005584 M2059
%S A005584 2,13,49,140,336,714,1386,2508,4290,7007,11011,16744,24752,35700,50388,
%T A005584 69768,94962,127281,168245,219604,283360,361790,457470,573300,712530,
%U A005584 878787,1076103,1308944,1582240,1901416
%N A005584 Coefficients of Chebyshev polynomials.
%C A005584 If X is an n-set and Y a fixed 2-subset of X then a(n-6) is equal to 
               the number of (n-6)-subsets of X intersecting Y. - Milan R. Janjic 
               (agnus(AT)blic.net), Jul 30 2007
%D A005584 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 797.
%D A005584 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005584 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A005584 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A005584 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A005584 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A005584 C. Rossiter, <a href="http://noticingnumbers.net/300SeriesCube.htm">Depictions, 
               Explorations and Formulas of the Euler/Pascal Cube</a>.
%H A005584 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A005584 G.f.: (2 - x) / ( 1 - x )^7.
%F A005584 a(n)=binomial(n+5, n-1)+binomial(n+4, n-1)=1/720*n*(n+11)*(n+4)*(n+3)*(n+2)*(n+1).
%F A005584 Binomial(n,6)+2*binomial(n,5), n>=5. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 26 2006
%p A005584 [seq(binomial(n,6)+2*binomial(n,5), n=5..35)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 26 2006
%p A005584 A005584:=(-2+z)/(z-1)**7; [S. Plouffe in his 1992 dissertation.]
%Y A005584 Sequence in context: A084156 A002534 A117717 this_sequence A072416 A056305 
               A056297
%Y A005584 Adjacent sequences: A005581 A005582 A005583 this_sequence A005585 A005586 
               A005587
%K A005584 nonn
%O A005584 1,1
%A A005584 N. J. A. Sloane (njas(AT)research.att.com).
%E A005584 More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), 
               Dec 07 1999.

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