OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..388
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(2*k,n-3*k)/k!.
MATHEMATICA
terms = 21; A[_] = 0; Do[A[x_] = Exp[x^3*A[x]^3 *(1+x* A[x])^2] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]*Range[0, terms-1]! (* Stefano Spezia, Oct 17 2025 *)
Table[n!*Sum[(n+1)^(k-1)*Binomial[2*k, n-3*k]/k!, {k, 0, Floor[n/3]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 06 2025 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\3, (n+1)^(k-1)*binomial(2*k, n-3*k)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 13 2025
STATUS
approved