OFFSET
0,3
FORMULA
a(0) = 1; a(n) = n! * Sum_{k=2..n} 2^(k-1)/(k-1) * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-k) * k! * |Stirling1(n-k,k)|/(n-k)!.
MATHEMATICA
With[{nn=20}, CoefficientList[Series[1/(1+x Log[1-2x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 11 2024 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\2, 2^(n-k)*k!*abs(stirling(n-k, k, 1))/(n-k)!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 04 2023
STATUS
approved