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A001701
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Generalized Stirling numbers.
(Formerly M4169 N1735)
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4
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1, 6, 26, 71, 155, 295, 511, 826, 1266, 1860, 2640, 3641, 4901, 6461, 8365, 10660, 13396, 16626, 20406, 24795, 29855, 35651, 42251, 49726, 58150, 67600, 78156
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| (1/24) n(n-1)(3n^2+17n+26), n>1.
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]
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MAPLE
| 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.]
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MATHEMATICA
| f[k_] := k + 1; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 30}] (* A001701 *)
(* Clark Kimberling, Dec 31 2011 *)
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CROSSREFS
| Equals A059302(n+2) + 1, n>1. Partial sums of A005564.
Sequence in context: A190095 A135036 A166796 * A175898 A094162 A172207
Adjacent sequences: A001698 A001699 A001700 * A001702 A001703 A001704
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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