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A000596
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Central factorial numbers.
(Formerly M3686 N1505)
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2
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4, 49, 273, 1023, 3003, 7462, 16422, 32946, 61446, 108031, 180895, 290745, 451269, 679644, 997084, 1429428, 2007768, 2769117, 3757117, 5022787, 6625311
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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REFERENCES
| J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
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.
Index entries for sequences related to factorial numbers
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FORMULA
| a(n) = 1/360*n*(n-1)*(n-2)*(2*n-1)*(2*n-3)*(5*n+1)
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MAPLE
| A000596:=-(4+21*z+14*z**2+z**3)/(z-1)**7; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| f[k_] := k^2; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 32}] (* A000596 *)
(* Clark Kimberling, Dec 31 2011 *)
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CROSSREFS
| a(n+1/2) = 1/16*A001823(n)
Column 2 of triangle A008955.
Sequence in context: A078187 A100256 A163944 * A113525 A064751 A045787
Adjacent sequences: A000593 A000594 A000595 * A000597 A000598 A000599
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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