A393977 G.f. A(x) satisfies A(x) = 1 - E^3(log(1 - x*A(x))), where E is the Euler operator x*d/dx.

1, 1, 12, 360, 23920, 3038275, 661613616, 227993931326, 117074972668864, 85514867404374267, 85632409776358310300, 114090874349629345407646, 197297302443962466857375808, 433713210324225209948611599324, 1190651062684690034955587638650576

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

G.f.: 1 + E^2(B(x)), where B(x) is the g.f. of A393475.

a(n) = n^2 * A393475(n) for n > 0.

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

Example

     -E(log(1 - x*A(x))) =     x +  3*x^2 +  40*x^3 +  1495*x^4 + ...
   -E^2(log(1 - x*A(x))) =     x +  6*x^2 + 120*x^3 +  5980*x^4 + ...
1 - E^3(log(1 - x*A(x))) = 1 + x + 12*x^2 + 360*x^3 + 23920*x^4 + ...

Prog

(PARI) E(f) = x*deriv(f);
my(A=1, N=20); for(k=1, N, A=1-E(E(E(log(1-x*A))))+x*O(x^N)); Vec(A)

Crossrefs

Cf. A003319, A393959, A394821.

Cf. A393475.

Sequence in context: A279182 A002674 A012552 * A012385 A012430 A012632

Adjacent sequences: A393974 A393975 A393976 * A393978 A393979 A393980

Keyword

nonn

Author

Seiichi Manyama, Apr 02 2026

Status

approved