|
%I #27 Feb 21 2021 06:06:48
%S 0,1,3,11,60,499,5705,82207,1419768,28501125,651233671,16676686707,
%T 472883844004,14705395791319,497538872883741,18193397941038751,
%U 714950006521386992,30046260016074301961,1344648068888240941035
%N Number of morphisms in full subcategories of Set spanned by {{}, {1}, {1, 2}, ..., {1, 2, ..., n}}.
%C For any natural number k, consider the set X_k={1,2,...,k}; in particular X_0 is empty. For any natural number n, let S_n be the full subcategory of Set spanned by the objects X_0, X_1,...,X_n. Then S_n has some number of morphisms, #S_n. When n=-1, we consider S_n to be empty. Our sequence is #S_{-1}, #S_0, #S_1, #S_2,....
%H Robert G. Wilson v, <a href="/A231344/b231344.txt">Table of n, a(n) for n = -1..386</a>
%F a(n)=sum_{0<=i,j<=n}i^j, where 0^0=1.
%e For n=2, we have 0^0+0^1+0^2+1^0+1^1+1^2+2^0+2^1+2^2=11.
%t a[n_] := 1 + Sum[i^j, {j, 0, n}, {i, n}]; a[-1] = 0; Array[a, 19, -1] (* _Robert G. Wilson v_, Feb 18 2014 *)
%o (PARI) a(n)=sum(i=0,n,sum(j=0,n,i^j)) \\ - _M. F. Hasler_, Nov 08 2013
%K nonn
%O -1,3
%A _David Spivak_, Nov 07 2013
%E More terms from _M. F. Hasler_, Nov 08 2013
|
