A387965 E.g.f. A(x) satisfies A(x) = exp( x^2*A(x)^2 / (1-x*A(x))^2 ) / (1-x*A(x)).

1, 1, 6, 66, 1068, 23040, 623640, 20343120, 777304080, 34065722880, 1684897532640, 92853166855680, 5642580362569920, 374876977113999360, 27033233358955824000, 2102994909138425702400, 175554183480419084140800, 15653676568509412392960000, 1484898987684110179698316800

Offset

0,3

Links

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

Formula

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

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

Mathematica

Table[n!*Sum[(n+1)^(k-1)*Binomial[2*n, n-2*k]/k!, {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Oct 27 2025 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (n+1)^(k-1)*binomial(2*n, n-2*k)/k!);
(Magma) [Factorial(n) * &+[(n+1)^(k-1)* Binomial(2*n, n-2*k) / Factorial(k) : k in [0..Floor(n/2)]] : n in [0..25] ]; // Vincenzo Librandi, Oct 27 2025

Crossrefs

Cf. A387964, A387966.

Cf. A361594.

Sequence in context: A128319 A174496 A008548 * A090358 A359462 A264407

Adjacent sequences: A387962 A387963 A387964 * A387966 A387967 A387968

Keyword

nonn

Author

Seiichi Manyama, Oct 12 2025

Status

approved