%I A001919 M4234 N1769
%S A001919 6,40,155,456,1128,2472,4950,9240,16302,27456,44473,69680,106080,157488,
%T A001919 228684,325584,455430,627000,850839,1139512,1507880,1973400,2556450,
%U A001919 3280680,4173390,5265936,6594165,8198880,10126336,12428768,15164952
%N A001919 Eighth column of quadrinomial coefficients.
%D A001919 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001919 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001919 L. Carlitz et al., Permutations and sequences with repetions by number 
               of increases, J. Combin. Theory, 1 (1966), 350-374.
%D A001919 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78.
%H A001919 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 A001919 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 A001919 a(n)= A008287(n, 7)= binomial(n+2, 5)*(n^2+21*n+180 )/42, n >= 3.
%F A001919 G.f.: (x^3)*(6-8*x+3*x^2 )/(1-x)^8. Numerator polynomial is N4(7, x) 
               from array A063421.
%F A001919 a(n)=n(n^2-1)(n^2-4)(n^2+21n+180)/5040 - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Jan 27 2005
%p A001919 seq(n*(n^2-1)*(n^2-4)*(n^2+21*n+180)/5040,n=3..34); (Deutsch)
%p A001919 A001919:=(3*z**2-8*z+6)/(z-1)**8; [Conjectured by S. Plouffe in his 1992 
               dissertation.]
%Y A001919 Sequence in context: A089207 A027777 A073773 this_sequence A005553 A055344 
               A059021
%Y A001919 Adjacent sequences: A001916 A001917 A001918 this_sequence A001920 A001921 
               A001922
%K A001919 nonn,easy
%O A001919 3,1
%A A001919 N. J. A. Sloane (njas(AT)research.att.com).
%E A001919 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 27 2005