A380425 - OEIS

%I #12 Jan 24 2025 11:59:53

%S 1,2,12,116,1592,28472,630028,16649348,512197456,17993496176,

%T 711065689364,31231930472492,1509776777566648,79670350504209896,

%U 4557716010219325468,280992142281969312548,18574365176584473753248,1310583528463442480750048,98318677221689347734929956

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

%H Seiichi Manyama, <a href="/A380425/b380425.txt">Table of n, a(n) for n = 0..360</a>

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A162695.

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

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

%Y Cf. A162695, A380426, A380427.

%Y Cf. A360474, A380406.

%K nonn,new

%O 0,2

%A _Seiichi Manyama_, Jan 24 2025