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Denominator of sum{k=1 to n} 1/s(n,k), where s(n,k) is an unsigned Stirling number of the first kind.
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%I #12 Aug 17 2019 03:25:12

%S 1,1,6,33,4200,4192200,1705200,77892963984,10086416728304192640,

%T 126556188275836361347200,451535899566923284351392000,

%U 1253032399528279799996000622278320876800

%N Denominator of sum{k=1 to n} 1/s(n,k), where s(n,k) is an unsigned Stirling number of the first kind.

%e a(4) = 33, the denominator of 1/6 + 1/11 + 1/6 + 1 = 47/33.

%e The first few fractions are: 1, 2, 11/6, 47/33, 4999/4200.

%p with(combinat): a:=n->denom(sum(1/abs(stirling1(n,k)),k=1..n)): seq(a(n),n=1..14); # _Emeric Deutsch_, Sep 02 2005

%t f[n_] := Sum[1/Abs[StirlingS1[n, k]], {k, n}]; Table[Denominator[f[n]], {n, 15}] (* _Ray Chandler_, Sep 02 2005 *)

%o (PARI) a(n) = denominator(sum(k=1, n, 1/abs(stirling(n,k,1)))); \\ _Michel Marcus_, Aug 17 2019

%Y Cf. A112288.

%K nonn,frac

%O 1,3

%A _Leroy Quet_, Sep 01 2005

%E Extended by _Emeric Deutsch_ and _Ray Chandler_, Sep 02 2005