A371342 - OEIS

%I #17 Mar 19 2024 09:26:20

%S 0,1,1,5,38,404,5514,91916,1810080,41119704,1058505600,30450551592,

%T 968121778128,33709242522864,1275738359407680,52141501470591360,

%U 2288907292892799744,107405692000948859904,5365016291068305805440,284225212617080543066880

%N E.g.f. satisfies A(x) = log(1 + x/(1 - A(x))).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F E.g.f.: Series_Reversion( (1 - x) * (exp(x) - 1) ).

%F a(n) = Sum_{k=1..n} (n+k-2)!/(n-1)! * Stirling1(n,k).

%F a(n) ~ LambertW(1)^n * n^(n-1) / (sqrt(1 + LambertW(1)) * exp(n) * (1 - LambertW(1))^(2*n-1)). - _Vaclav Kotesovec_, Mar 19 2024

%t Table[Sum[(n+k-2)! / (n-1)! * StirlingS1[n,k], {k,1,n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Mar 19 2024 *)

%o (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(serreverse((1-x)*(exp(x)-1)))))

%o (PARI) a(n) = sum(k=1, n, (n+k-2)!/(n-1)!*stirling(n, k, 1));

%Y Cf. A370922, A371326.

%Y Cf. A052842, A052892.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Mar 19 2024