A387948 E.g.f. A(x) satisfies A(x) = exp( x^2*A(x)^2 / (1 - x*A(x))^2 ).

1, 0, 2, 12, 132, 1920, 34680, 756000, 19288080, 564157440, 18617588640, 684413452800, 27739649931840, 1229021283409920, 59098102112649600, 3065382777468211200, 170608657948836307200, 10142078316527930572800, 641371064635390382092800, 42992863354008994922496000

Offset

0,3

Links

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

Formula

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

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

Mathematica

Table[n!*Sum[(n+1)^(k-1)*Binomial[n-1, 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(n-1, n-2*k)/k!);
(Magma) [Factorial(n) * &+[(n+1)^(k-1)* Binomial(n-1, n-2*k) / Factorial(k) : k in [0..Floor(n/2)]] : n in [0..25] ]; // Vincenzo Librandi, Oct 27 2025

Crossrefs

Cf. A376474, A387949.

Cf. A364939, A387950.

Cf. A364941.

Sequence in context: A258467 A286422 A073551 * A215363 A200319 A213640

Adjacent sequences: A387945 A387946 A387947 * A387949 A387950 A387951

Keyword

nonn

Author

Seiichi Manyama, Oct 12 2025

Status

approved