/usr/share/openturns/validation/validEnumerate.txt is in openturns-validation 1.5-7build2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 | > restart:
> f:=GAMMA(n+d+1)/GAMMA(n+1)/GAMMA(d+1):
> p:=convert(series(f,n,2),polynom):
> sol:=solve(p=k,n);
> with(plots):
> plot3d(f-p,n=0..5,d=0..5,axes=boxed);
-1 + k
sol := ------------------
Psi(d + 1) + gamma
> assume(n,integer,d,integer);convert(f,factorial);
(n~ + d~)!
----------
n~! d~!
> product((n+k)/k,k=1..d);
GAMMA(n~ + d~ + 1)
---------------------------
GAMMA(n~ + 1) GAMMA(1 + d~)
> for i from 1 to 5 do
> expand(subs(n=i,f));
> od;
1 + d~
2
1 + 3/2 d~ + 1/2 d~
2 3
1 + 11/6 d~ + d~ + 1/6 d~
25 35 2 3 4
1 + -- d~ + -- d~ + 5/12 d~ + 1/24 d~
12 24
137 2 17 3 4 5
1 + --- d~ + 15/8 d~ + -- d~ + 1/8 d~ + 1/120 d~
60 24
>
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