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)^3) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (n+1)^(k-1) * binomial(2*n+k,n-2*k)/k!.
MATHEMATICA
Table[n!*Sum[(n+1)^(k-1)*Binomial[2*n+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+k, n-2*k)/k!);
(Magma) [Factorial(n) * &+[(n+1)^(k-1)* Binomial(2*n+k, n-2*k) / Factorial(k) : k in [0..Floor(n/2)]] : n in [0..25] ]; // Vincenzo Librandi, Oct 27 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 12 2025
STATUS
approved
