A007322 Number of functors of degree n from free Abelian groups to Abelian groups.
1, 6, 39, 320, 3281, 40558, 586751, 9719616, 181353777, 3762893750, 85934344775, 2141853777856, 57852105131809, 1683237633305502, 52483648929669119, 1745835287515739328, 61712106494672572641, 2309989101145068446502, 91279147976756195994983
Offset: 1
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
Programs
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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 *)
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
Extensions
More terms from Vladeta Jovovic, Aug 17 2006