%I #15 Oct 20 2015 17:29:54

%S 1,1,5,54,1004,28500,1145220,61822320,4314308544,377894704320,

%T 40585486536000,5244015013776000,802446580009071360,

%U 143506045946368385280,29655761650514250451200,7012678074108426720000000

%N a(n) = (n+1)! * int(Gamma(n+x)/Gamma(x), x = 0..1).

%C The factor (n+1)! normalizes the sequence to integers.

%C E.g.f. for a(n)/(n+1)!: x/((x-1)*log(1-x)).

%H Vaclav Kotesovec, <a href="/A245765/b245765.txt">Table of n, a(n) for n = 0..200</a>

%t a[n_] := (n+1)! Integrate[Pochhammer[x, n], {x, 0, 1}]; Table[a[n], {n, 0, 20}]

%t Table[(n+1)! * Sum[(-1)^(n-k) * StirlingS1[n,k] / (k+1),{k,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Aug 03 2014 *)

%Y Cf. A000142.

%K nonn,easy

%O 0,3

%A _Vladimir Reshetnikov_, Jul 31 2014