A300598 - OEIS

%I #7 Mar 09 2018 22:04:28

%S 1,1,9,184,6105,285909,17599855,1366487208,130312110537,

%T 14977420657205,2044343858148526,327321396575462328,

%U 60816978336055883851,12988287586752637095951,3161098207809674432144760,870056671853543460441640960,268957112246197632099231284121,92799365448465489168470692401021,35538203127994691420731763316052499,15028828305943284874962308136851532840

%N a(n) = A300591(n) / n for n>=1.

%C If G(x) satisfies: [x^n] exp (n^2 * G(x) ) = n^2 * [x^(n-1)] exp( n^2 * G(x) ) for n>=1, then G(x) equals the o.g.f. of A300591.

%H Paul D. Hanna, <a href="/A300598/b300598.txt">Table of n, a(n) for n = 1..200</a>

%o (PARI) {a(n) = my(A=[1]); for(i=1, n+1, A=concat(A, 0); V=Vec(Ser(A)^((#A-1)^2)); A[#A] = ((#A-1)^2*V[#A-1] - V[#A])/(#A-1)^2 ); (1/n)*polcoeff( log(Ser(A)), n)}

%o for(n=1, 30, print1(a(n), ", "))

%Y Cf. A300591.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Mar 09 2018