A379684 - OEIS

%I #8 Dec 30 2024 02:17:00

%S 1,0,3,11,193,2389,50191,1088205,29836353,902845673,31428924631,

%T 1207426391137,51394833121105,2386048646491197,120379283952129567,

%U 6547887322803355589,382306453347573490177,23839225109022069540817,1581540933047988924532135

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

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

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

%Y Cf. A213644, A377890, A379685.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Dec 29 2024