A376040 - OEIS

%I #8 Sep 07 2024 16:01:46

%S 0,1,7,119,3258,123414,5978082,352880562,24573720672,1972239280488,

%T 179250831525720,18197871488362752,2041093578923498448,

%U 250654006995798120480,33449544716000374458000,4819960747934844400104480,745867334512204468875843840

%N E.g.f. satisfies A(x) = -log(1 - x / (1 - A(x))^3).

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

%F E.g.f.: Series_Reversion( (1 - x)^3 * (1 - exp(-x)) ).

%F a(n) = Sum_{k=1..n} (3*n+k-2)!/(3*n-1)! * |Stirling1(n,k)|.

%o (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(serreverse((1-x)^3*(1-exp(-x))))))

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

%Y Cf. A376038, A376039, A376041.

%Y Cf. A371370.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 07 2024