A376558 - OEIS

%I #11 Sep 28 2024 10:42:38

%S 1,1,3,22,245,3576,65527,1449904,37596393,1118442880,37559084651,

%T 1405597826304,58012540741597,2617923512200192,128240561732097375,

%U 6777245042104293376,384358793388984148433,23284761629109883600896,1500714780345430134323923

%N E.g.f. satisfies A(x) = exp( x*A(x) / (1 - x^2*A(x)^2) ).

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

%F E.g.f.: (1/x) * Series_Reversion( x*exp(-x / (1 - x^2)) ).

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

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

%Y Cf. A052873, A376563.

%Y Cf. A088009, A376474.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 28 2024