A393475 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.

1, 1, 3, 40, 1495, 121531, 18378156, 4652937374, 1829296447951, 1055739103757707, 856324097763583103, 942899788013465664526, 1370120155860850464287332, 2566350356948078165376399996, 6074750319819847117120345095156, 17866277583553806453770008420577710

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

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

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

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).

Prog

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

Crossrefs

Cf. A393977.

Sequence in context: A110468 A327356 A396922 * A385387 A295612 A350545

Adjacent sequences: A393472 A393473 A393474 * A393476 A393477 A393478

Keyword

nonn

Author

Seiichi Manyama, Apr 03 2026

Status

approved