OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
FORMULA
E.g.f. A(x) satisfies A(x) = 1/(1 - x*A(x)*(exp(x*A(x))-1)^2).
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (2*k)!/k! * (n+k)! * Stirling2(n-k,2*k)/(n-k)!.
MATHEMATICA
Table[(1/(n+1))* Sum[(2*k)!/k!*(n+k)!*StirlingS2[n-k, 2*k]/(n-k)!, {k, 0, Floor[n/3]}], {n, 0, 21}] (* Vincenzo Librandi, Feb 13 2026 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x)-1)^2))/x))
(Magma) [(1/(n+1)) * &+[Factorial(2*k) / Factorial(k) * Factorial(n+k)* StirlingSecond(n-k, 2*k)/Factorial(n-k): k in [0..Floor(n/3)]]: n in [0..25] ]; // Vincenzo Librandi, Feb 13 2026
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 22 2026
STATUS
approved