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A007322 Number of functors of degree n from free Abelian groups to Abelian groups.
(Formerly M4231)
4
1, 6, 39, 320, 3281, 40558, 586751, 9719616, 181353777, 3762893750, 85934344775, 2141853777856, 57852105131809, 1683237633305502, 52483648929669119, 1745835287515739328, 61712106494672572641, 2309989101145068446502, 91279147976756195994983 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

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).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..400

Vaclav Kotesovec, Asymptotics of the sequence A120733

FORMULA

Binomial transform of A101370. - Vladeta Jovovic, Aug 17 2006

a(n) = (1/n!)*Sum_{k=1..n} (-1)^(n-k)*Stirling1(n+1,k+1)*A000670(k)^2. - Vladeta Jovovic, Aug 17 2006

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

Partial sums of A120733. - Vladeta Jovovic, Aug 21 2006

a(n) ~ 2^(log(2)/2-2) * n! / (log(2))^(2*n+2). - Vaclav Kotesovec, May 03 2015

MATHEMATICA

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-Fran├žois Alcover, May 15 2012, after Vladeta Jovovic *)

CROSSREFS

Sequence in context: A067273 A187117 A137972 * A058191 A113347 A265953

Adjacent sequences:  A007319 A007320 A007321 * A007323 A007324 A007325

KEYWORD

nonn,nice

AUTHOR

Don Zagier (don.zagier(AT)mpim-bonn.mpg.de), Apr 11 1994

EXTENSIONS

More terms from Vladeta Jovovic, Aug 17 2006

STATUS

approved

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Last modified January 21 17:07 EST 2019. Contains 319350 sequences. (Running on oeis4.)