A393475 - OEIS

%I #32 Apr 03 2026 10:06:49

%S 1,1,3,40,1495,121531,18378156,4652937374,1829296447951,

%T 1055739103757707,856324097763583103,942899788013465664526,

%U 1370120155860850464287332,2566350356948078165376399996,6074750319819847117120345095156,17866277583553806453770008420577710

%N G.f. A(x) satisfies A(x) = 1 - E(log(1 - x*(1 + E^2(A(x))))), where E is the Euler operator x*d/dx.

%F G.f. A(x) satisfies A(x) = 1 + x*A(x)*(1 + E^2(A(x))) + x*E^3(A(x)).

%F G.f.: 1 - E(log(1 - x*B(x))), where B(x) is the g.f. of A393977.

%F a(0) = 1; a(n) = ((n-1)^3+1) * a(n-1) + Sum_{k=1..n-1} k^2 * a(k) * a(n-1-k).

%o (PARI) E(f) = x*deriv(f);

%o my(A=1, N=20); for(k=1, N, A=1+x*A*(1+E(E(A)))+x*E(E(E(A)))+x*O(x^N)); Vec(A)

%Y Cf. A393977.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 03 2026