A389867 E.g.f. A(x) satisfies A(x) = exp( x^2 * A(x) / (1-x)^2 ) / (1-x).

1, 1, 4, 30, 300, 3780, 58080, 1056720, 22251600, 532843920, 14309900640, 426162068640, 13943485765440, 497318845383360, 19208006841703680, 798792334006867200, 35590619106339897600, 1691606283967375776000, 85439253017472440486400, 4570109517978497074982400

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

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

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

Mathematica

Table[n!*Sum[(k+1)^(k-1)*Binomial[n+k, n-2*k]/k!, {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Oct 28 2025 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(k-1)*binomial(n+k, n-2*k)/k!);
(Magma) [Factorial(n) * &+[(k+1)^(k-1)* Binomial(n+k, n-2*k) / Factorial(k) : k in [0..Floor(n/2)]] : n in [0..25] ]; // Vincenzo Librandi, Oct 28 2025

Crossrefs

Cf. A371038, A378094, A389868.

Sequence in context: A347994 A240958 A054972 * A052452 A348708 A379190

Adjacent sequences: A389864 A389865 A389866 * A389868 A389869 A389870

Keyword

nonn

Author

Seiichi Manyama, Oct 18 2025

Status

approved