A390184 E.g.f. A(x) satisfies A(x) = exp( x/(1-x^3)^2 * A(x) ).

1, 1, 3, 16, 173, 2016, 28327, 487264, 9742329, 221970016, 5695274411, 162587676384, 5111837454517, 175549536496816, 6539363083186767, 262652023656051376, 11315735944857843953, 520566507042182202816, 25470084710826749361619, 1320718835171918257741504

Offset

0,3

Links

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

Formula

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

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

Mathematica

Table[n!*Sum[(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 03 2025 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\3, (n-3*k+1)^(n-3*k-1)*binomial(2*n-5*k-1, k)/(n-3*k)!);
(Magma) [Factorial(n) * &+[(n-3*k+1)^(n-3*k-1)* Binomial(2*n-5*k-1, k) / Factorial(n-3*k) : k in [0..Floor(n/3)]] : n in [0..25] ]; // Vincenzo Librandi, Nov 03 2025

Crossrefs

Cf. A376576, A390014, A390015, A390185.

Sequence in context: A297668 A203593 A389987 * A304902 A024041 A152554

Adjacent sequences: A390181 A390182 A390183 * A390185 A390186 A390187

Keyword

nonn

Author

Seiichi Manyama, Oct 28 2025

Status

approved