Search: id:A001701
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%I A001701 M4169 N1735
%S A001701 1,6,26,71,155,295,511,826,1266,1860,2640,3641,4901,6461,8365,10660,
%T A001701 13396,16626,20406,24795,29855,35651,42251,49726,58150,67600,78156
%N A001701 Generalized Stirling numbers.
%D A001701 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001701 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001701 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 A001701 Mitrinovic, D. S.; Mitrinovic, R. S.; Tableaux d'une classe de nombres 
               relies aux nombres de Stirling. Univ. Beograd. Publ. Elektrotehn. 
               Fak. Ser. Mat. Fiz. No. 77 1962, 77 pp.
%H A001701 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 A001701 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 A001701 (1/24) n(n-1)(3n^2+17n+26), n>1.
%F A001701 If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,
               j=0..k-1),k=0..n-i), then a(n) = f(n,n-2,2), for n>=2. [From Milan 
               R. Janjic (agnus(AT)blic.net), Dec 20 2008]
%p A001701 A001701:=(-1-z-6*z**2+9*z**3-5*z**4+z**5)/(z-1)**5; [Conjectured by S. 
               Plouffe in his 1992 dissertation.]
%Y A001701 Equals A059302(n+2) + 1, n>1. Partial sums of A005564.
%Y A001701 Sequence in context: A136892 A135036 A166796 this_sequence A094162 A060101 
               A036422
%Y A001701 Adjacent sequences: A001698 A001699 A001700 this_sequence A001702 A001703 
               A001704
%K A001701 nonn
%O A001701 1,2
%A A001701 N. J. A. Sloane (njas(AT)research.att.com).

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