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A007322
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Number of functors of degree n from free Abelian groups to Abelian groups.
(Formerly M4231)
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4
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1, 6, 39, 320, 3281, 40558, 586751, 9719616, 181353777, 3762893750, 85934344775, 2141853777856, 57852105131809, 1683237633305502, 52483648929669119, 1745835287515739328, 61712106494672572641, 2309989101145068446502, 91279147976756195994983
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OFFSET
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1,2
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REFERENCES
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H. J. Baues, Quadratic functors and metastable homotopy, Jnl. Pure and Applied Algebra, 91 (1994), 49-107.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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G.f.: (1/(1-x))*Sum_{m>0,n>0} Sum_{j=1..n} (-1)^(n-j)*binomial(n,j)*((1-x)^(-j)-1)^m. - Vladeta Jovovic, Aug 17 2006
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MATHEMATICA
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A120733[n_] := A120733[n] = Sum[2^(-2-r-s)*Binomial[n+r*s-1, n] , {r, 0, Infinity}, {s, 0, Infinity}]; a[n_] := Sum[A120733[k], {k, 1, n}]; Table[Print[an = a[n]]; an, {n, 1, 18}] (* Jean-François Alcover, May 15 2012, after Vladeta Jovovic *)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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Don Zagier (don.zagier(AT)mpim-bonn.mpg.de), Apr 11 1994
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EXTENSIONS
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STATUS
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approved
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