Search: id:A005587
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%I A005587 M4929
%S A005587 0,14,42,90,165,275,429,637,910,1260,1700,2244,2907,3705,4655,5775,7084,
%T A005587 8602,10350,12350,14625,17199,20097,23345,26970,31000,35464,40392,45815,
%U A005587 51765,58275,65379,73112,81510,90610,100450,111069,122507,134805,148005
%N A005587 n(n+5)(n+6)(n+7)/24.
%C A005587 a(n) = number of Standard Young Tableaux of shape (n+3,4). - David Callan 
               (callan(AT)stat.wisc.edu), Aug 17 2004
%D A005587 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005587 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 796.
%H A005587 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 A005587 R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">J. Integer Seqs., Vol. 3 (2000), #00.1.6</
               a>
%H A005587 Matthew M. Conroy, <a href="http://www.madandmoonly.com/doctormatt">Home 
               page</a> (listed instead of email address)
%H A005587 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 A005587 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.
%F A005587 G.f.: (14 - 28x + 20x^2 - 5x^3) / (1 - x)^5.
%F A005587 C(7+n, 4)-C(7+n, 3) - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Dec 09 2005
%p A005587 A005587:=z*(-14+28*z-20*z**2+5*z**3)/(z-1)**5; [S. Plouffe in his 1992 
               dissertation.]
%p A005587 seq(numbperm(n,4)/24-numbperm(n,3)/6, n=7..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               May 20 2008
%p A005587 a:=n->(sum(numbcomp(n,4), j=9..n)):seq(a(n)/4, n=8..47);# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Aug 26 2008]
%Y A005587 Fifth diagonal of Catalan triangle A033184. Fifth column of Catalan triangle 
               A009766.
%Y A005587 Numerator polynomial 14 - 28x + 20x^2 - 5x^3 from fourth row of triangle 
               A062991.
%Y A005587 Sequence in context: A064512 A118237 A163756 this_sequence A120714 A041378 
               A041380
%Y A005587 Adjacent sequences: A005584 A005585 A005586 this_sequence A005588 A005589 
               A005590
%K A005587 nonn,easy
%O A005587 0,2
%A A005587 N. J. A. Sloane (njas(AT)research.att.com).
%E A005587 M4929 (this sequence) and M4930 were the same.
%E A005587 More terms from Matthew Conroy (list1(AT)madandmoonly.com), Jan 16 2006
%E A005587 Plouffe Maple line edited by N. J. A. Sloane (njas(AT)research.att.com), 
               May 13 2008

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