A007322 Number of functors of degree n from free Abelian groups to Abelian groups. (Formerly M4231)

1, 6, 39, 320, 3281, 40558, 586751, 9719616, 181353777, 3762893750, 85934344775, 2141853777856, 57852105131809, 1683237633305502, 52483648929669119, 1745835287515739328, 61712106494672572641, 2309989101145068446502, 91279147976756195994983

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-François Alcover, May 15 2012, after Vladeta Jovovic *)

Crossrefs

Sequence in context: A067273 A187117 A137972 * A341728 A058191 A113347

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