A370994 - OEIS

%I #11 Mar 07 2024 01:32:43

%S 1,0,0,6,12,40,3060,23688,191520,9698400,158548320,2304973440,

%T 100716073920,2627516361600,58513944513024,2512156283683200,

%U 89046056086041600,2739316757454950400,124170651534918297600,5440968468533003212800,215067442349096186572800

%N Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x^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..floor(n/3)} (n+k)! * |Stirling1(n-2*k,k)|/(n-2*k)!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x^2*log(1-x)))/x))

%o (PARI) a(n) = sum(k=0, n\3, (n+k)!*abs(stirling(n-2*k, k, 1))/(n-2*k)!)/(n+1);

%Y Cf. A052802, A370993, A370995.

%Y Cf. A351503, A370989.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Mar 06 2024