OFFSET
0,3
FORMULA
a(n) = Sum_{k=1..n} (3*k-2)!/(2*k-1)! * Stirling2(n,k).
a(n) ~ sqrt(31) * n^(n-1) / (sqrt(2) * 3^(3/2) * log(31/27)^(n - 1/2) * exp(n)). - Vaclav Kotesovec, Mar 19 2024
E.g.f.: Series_Reversion( log(1 + x * (1 - x)^2) ). - Seiichi Manyama, Sep 08 2024
MATHEMATICA
Table[Sum[(3*k-2)!/(2*k-1)! * StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 19 2024 *)
PROG
(PARI) a(n) = sum(k=1, n, (3*k-2)!/(2*k-1)!*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 18 2024
STATUS
approved