A377890 - OEIS

%I #11 Dec 29 2024 08:48:54

%S 1,2,15,211,4433,124741,4412815,188335981,9421966209,540884623753,

%T 35054089163351,2531882857204273,201689970517618225,

%U 17567711167993834381,1661084543502646535967,169448367505003640681221,18550123929621138841581185,2169272360350263071212545553

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

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

%F E.g.f.: (1/x) * Series_Reversion( x * (exp(-x) - x) ). - _Seiichi Manyama_, Dec 29 2024

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

%Y Cf. A088690, A377826, A377891.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 11 2024