A387950 E.g.f. A(x) satisfies A(x) = exp( x^3*A(x)^3 / (1 - x*A(x))^2 ).

1, 0, 0, 6, 48, 360, 5400, 105840, 2056320, 44876160, 1166659200, 33889363200, 1065718684800, 36625260672000, 1374104225894400, 55590719414630400, 2408356088506368000, 111457856780734464000, 5490493391333247897600, 286654692243439263744000

Offset

0,4

Links

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

Formula

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

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

Mathematica

Table[n!*Sum[(n+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, (n+1)^(k-1)*binomial(n-k-1, n-3*k)/k!);
(Magma) [Factorial(n) * &+[(n+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. A376475, A387951.

Cf. A364939, A387948.

Cf. A389348.

Sequence in context: A324074 A052625 A389845 * A326888 A326895 A291033

Adjacent sequences: A387947 A387948 A387949 * A387951 A387952 A387953

Keyword

nonn

Author

Seiichi Manyama, Oct 12 2025

Status

approved