A387976 E.g.f. A(x) satisfies A(x) = exp( x^2*A(x)^2 ) / (1-x*A(x)).

1, 1, 6, 54, 756, 13920, 322680, 9003120, 294270480, 11029858560, 466544262240, 21986317140480, 1142480739597120, 64902023193047040, 4001773001898672000, 266174759437774387200, 18997883241131015020800, 1448333175318024477081600, 117462983954688152632051200

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) ).

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

Mathematica

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

Crossrefs

Cf. A387964, A387965, A387966.

Cf. A377831, A380718.

Sequence in context: A167571 A366232 A138434 * A360545 A217238 A378026

Adjacent sequences: A387973 A387974 A387975 * A387977 A387978 A387979

Keyword

nonn

Author

Seiichi Manyama, Oct 13 2025

Status

approved