A389845 E.g.f. A(x) satisfies A(x) = exp(x^3 * A(x) / (1-x)^2).

1, 0, 0, 6, 48, 360, 3960, 55440, 846720, 14394240, 277603200, 5947603200, 139169923200, 3541099161600, 97552507852800, 2891006492774400, 91678434591744000, 3098748873572352000, 111234903008618188800, 4226208270332022374400, 169436986909087113216000

Offset

0,4

Links

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

Formula

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

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

Mathematica

Table[n!*Sum[(k+1)^(k-1)*Binomial[n-k-1, n-3*k]/k!, {k, 0, Floor[n/3]}], {n, 0, 25}] (* Vincenzo Librandi, Oct 28 2025 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\3, (k+1)^(k-1)*binomial(n-k-1, n-3*k)/k!);
(Magma) [Factorial(n) * &+[(k+1)^(k-1)* Binomial(n-k-1, n-3*k) / Factorial(k) : k in [0..Floor(n/3)]] : n in [0..25] ]; // Vincenzo Librandi, Oct 28 2025

Crossrefs

Cf. A362775, A389843.

Cf. A378095.

Sequence in context: A052571 A324074 A052625 * A387950 A326888 A326895

Adjacent sequences: A389842 A389843 A389844 * A389846 A389847 A389848

Keyword

nonn

Author

Seiichi Manyama, Oct 17 2025

Status

approved