OFFSET
0,5
FORMULA
E.g.f. satisfies log(A(x)) = -log(1 - x * A(x))^3 / 6.
a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n+1)^(k-1) * |Stirling1(n,3*k)|/(6^k * k!).
MATHEMATICA
m = 22; (* number of terms *)
A[_] = 0;
Do[A[x_] = 1/(1 - x*A[x])^(Log[1 - x*A[x]]^2/6) + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Sep 12 2022 *)
PROG
(PARI) a(n) = sum(k=0, n\3, (3*k)!*(n+1)^(k-1)*abs(stirling(n, 3*k, 1))/(6^k*k!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 09 2022
STATUS
approved