OFFSET
0,3
FORMULA
E.g.f. satisfies A(x) = log(1 + x * exp(3 * A(x))).
a(n) = Sum_{k=1..n} (2 * n)^(k-1) * |Stirling1(n,k)|.
a(n) = Sum_{k=1..n} (3 * n)^(k-1) * Stirling1(n,k).
a(n) = Product_{k=2*n+1..3*n-1} k = (3*n-1)!/(2*n)! for n > 0.
E.g.f.: Series_Reversion( exp(-3*x) * (exp(x) - 1) ). - Seiichi Manyama, Sep 10 2024
PROG
(PARI) a(n) = sum(k=1, n, (2*n)^(k-1)*abs(stirling(n, k, 1)));
(PARI) a(n) = sum(k=1, n, (3*n)^(k-1)*stirling(n, k, 1));
(PARI) a(n) = if(n==0, 0, (3*n-1)!/(2*n)!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 26 2022
STATUS
approved