A364978 - OEIS

%I #8 Aug 15 2023 07:42:01

%S 1,1,2,15,124,1565,23886,446887,9787352,246408633,7010910010,

%T 222438284651,7788393551412,298293192119221,12406118302851014,

%U 556817903190669135,26825727269937929776,1380790608848655193457,75625529930102546486514

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

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

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

%Y Cf. A161631, A364979.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 15 2023