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A087761 Expansion of (1-x)^(1/(x-1)).

%I A087761 #22 Sep 22 2021 10:29:23
%S A087761 1,1,4,21,140,1130,10674,115206,1396016,18739080,275712840,4408612560,
%T A087761 76070179272,1408041937848,27816773482848,583970117197320,
%U A087761 12978149959718400,304310928180279360,7506092106055537344
%N A087761 Expansion of (1-x)^(1/(x-1)).
%H A087761 Seiichi Manyama, <a href="/A087761/b087761.txt">Table of n, a(n) for n = 0..439</a>
%F A087761 a(n) = Sum_{k=0..n} |Stirling1(n, k)|*A000248(k).
%F A087761 From _Paul D. Hanna_, Mar 17 2010: (Start)
%F A087761 E.g.f.: exp( Sum_{n>=1} H(n)*x^n ) where H(n) is the n-th harmonic number;
%F A087761 a(n) = (n-1)!*Sum_{k=0..n-1} (n-k)*H(n-k)*a(k)/k! for n>0 with a(0)=1. (End)
%F A087761 Empirical: a(n) = Sum_{i=0..n} binomial(n,i)*A005727(i)*(n-1)!/(i-1)! for n>0. - _John M. Campbell_, Dec 13 2016
%t A087761 Table[Sum[BellY[n, k, Table[m! HarmonicNumber[m], {m, n}]], {k, 0, n}], {n, 0, 20}] (* _Vladimir Reshetnikov_, Nov 09 2016 *)
%o A087761 (PARI) a(n)=if(n==0,1,(n-1)!*sum(k=0,n-1,(n-k)*sum(j=1,n-k,1/j)*a(k)/k!)) \\ _Paul D. Hanna_, Mar 17 2010; corrected Mar 19 2010
%Y A087761 Cf. A000248, A005727.
%K A087761 nonn
%O A087761 0,3
%A A087761 _Vladeta Jovovic_, Oct 02 2003