A390272 E.g.f. A(x) satisfies A(x) = exp( x / (1+x^3)^2 * A(x)^2 ).

1, 1, 5, 49, 681, 13441, 336013, 10181025, 362152913, 14800216897, 683416124181, 35192610816529, 1999704346712185, 124289978967627201, 8388496934772060317, 610953501719493093121, 47762129258134699822497, 3989238163603650826552705, 354531079431585063672998437

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..345

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k * (2*(n-3*k)+1)^(n-3*k-1) * binomial(2*n-5*k-1,k)/(n-3*k)!.

E.g.f.: exp( -LambertW(-2*x / (1+x^3)^2)/2 ).

Mathematica

Table[n!*Sum[(-1)^k*(2*(n-3*k)+1)^(n-3*k-1)*Binomial[2*n-5*k-1, k]/(n-3*k)!, {k, 0, Floor[n/3]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 05 2025 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\3, (-1)^k*(2*(n-3*k)+1)^(n-3*k-1)*binomial(2*n-5*k-1, k)/(n-3*k)!);

Crossrefs

Cf. A390063, A390270.

Cf. A390059, A390271.

Cf. A390216.

Sequence in context: A116873 A324361 A387916 * A089914 A267220 A052142

Adjacent sequences: A390269 A390270 A390271 * A390273 A390274 A390275

Keyword

nonn

Author

Seiichi Manyama, Oct 30 2025

Status

approved