A370939 - OEIS

%I #10 Mar 06 2024 07:59:52

%S 1,1,7,93,1848,49194,1646352,66471138,3145730760,170825968008,

%T 10472450056632,715494753359352,53913145327125840,4441896708946850880,

%U 397268517350608957440,38332384702788360859344,3969252425402471222357760,439043217473917940361120000

%N Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + log(1-3*x)/3) ).

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

%F a(n) = (1/(n+1)!) * Sum_{k=0..n} 3^(n-k) * (n+k)! * |Stirling1(n,k)|.

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+log(1-3*x)/3))/x))

%o (PARI) a(n) = sum(k=0, n, 3^(n-k)*(n+k)!*abs(stirling(n, k, 1)))/(n+1)!;

%Y Cf. A052802, A370938.

%Y Cf. A370934, A370937.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 06 2024