%I M4231 #20 Oct 07 2017 00:09:58

%S 1,6,39,320,3281,40558,586751,9719616,181353777,3762893750,

%T 85934344775,2141853777856,57852105131809,1683237633305502,

%U 52483648929669119,1745835287515739328,61712106494672572641,2309989101145068446502,91279147976756195994983

%N Number of functors of degree n from free Abelian groups to Abelian groups.

%D H. J. Baues, Quadratic functors and metastable homotopy, Jnl. Pure and Applied Algebra, 91 (1994), 49-107.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A007322/b007322.txt">Table of n, a(n) for n = 1..400</a>

%H Vaclav Kotesovec, <a href="http://oeis.org/A120733/a120733.pdf">Asymptotics of the sequence A120733</a>

%F Binomial transform of A101370. - _Vladeta Jovovic_, Aug 17 2006

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

%F 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

%F Partial sums of A120733. - _Vladeta Jovovic_, Aug 21 2006

%F a(n) ~ 2^(log(2)/2-2) * n! / (log(2))^(2*n+2). - _Vaclav Kotesovec_, May 03 2015

%t 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_ *)

%K nonn,nice

%O 1,2

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

%E More terms from _Vladeta Jovovic_, Aug 17 2006