OFFSET
0,3
FORMULA
a(n) = Sum_{k=1..n} (3*k-2)!/(2*k-1)! * |Stirling1(n,k)|.
a(n) ~ n^(n-1) / (sqrt(2) * (exp(4/27) - 1)^(n - 1/2) * exp(23*n/27)). - Vaclav Kotesovec, Mar 19 2024
E.g.f.: Series_Reversion( 1 - exp(-x * (1 - x)^2) ). - Seiichi Manyama, Sep 08 2024
MAPLE
A371314 := proc(n)
add((3*k-2)!/(2*k-1)!*abs(stirling1(n, k)), k=1..n) ;
end proc:
seq(A371314(n), n=0..40) ; # R. J. Mathar, Mar 25 2024
MATHEMATICA
Table[Sum[(3*k-2)!/(2*k-1)! * Abs[StirlingS1[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)!*abs(stirling(n, k, 1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 18 2024
STATUS
approved