A370941 - OEIS

%I #10 Mar 06 2024 07:59:32

%S 1,2,18,304,7668,259048,11001968,563728464,33857839360,2333472749376,

%T 181558569560448,15743501573763456,1505641080366272640,

%U 157445985444107880960,17872580693502293022720,2188829492626563123881472,287673783237906407512565760

%N Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + 2*log(1-x)) ).

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

%F a(n) = (1/(n+1)!) * Sum_{k=0..n} 2^k * (n+k)! * |Stirling1(n,k)|.

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+2*log(1-x)))/x))

%o (PARI) a(n) = sum(k=0, n, 2^k*(n+k)!*abs(stirling(n, k, 1)))/(n+1)!;

%Y Cf. A258922, A370940.

%Y Cf. A370938.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 06 2024