%I A002419 M4699 N2008
%S A002419 1,10,40,110,245,476,840,1380,2145,3190,4576,6370,8645,11480,14960,
%T A002419 19176,24225,30210,37240,45430,54901,65780,78200,92300,108225,126126,
%U A002419 146160,168490,193285,220720,250976,284240,320705,360570,404040,451326
%N A002419 4-dimensional figurate numbers: (6n-2)*C(n+2,3)/4.
%D A002419 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002419 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002419 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A002419 A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, 
               p. 195.
%H A002419 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 A002419 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 A002419 a(n)= (3*n-1)*binomial(n+2, 3)/2, n>=1. G.f.: x*(1+5*x)/(1-x)^5.
%p A002419 A002419:=-(1+5*z)/(z-1)**5; [Conjectured by S. Plouffe in his 1992 dissertation.]
%Y A002419 Cf. A093563 ((6, 1) Pascal, column m=4). A002414 (differences).
%Y A002419 Sequence in context: A131037 A071233 A063490 this_sequence A027981 A013977 
               A075060
%Y A002419 Adjacent sequences: A002416 A002417 A002418 this_sequence A002420 A002421 
               A002422
%K A002419 nonn,easy
%O A002419 1,2
%A A002419 N. J. A. Sloane (njas(AT)research.att.com).
%E A002419 More terms from Pab Ter (pabrlos(AT)yahoo.com), May 08 2004