A295578 a(1)=1; thereafter, a(n+1) = Sum_{d divides n} (n!/(d!*(n/d)!))*(n/d)*a(d).

1, 1, 3, 6, 22, 27, 573, 580, 14028, 104757, 845647, 845658, 120596070, 120596083, 10092478017, 157205844432, 1332037102048, 1332037102065, 395631664423683, 395631664423702, 170313938200001322, 3110070531413441343, 26922450918793025365, 26922450918793025388, 10816813121713202599812

Offset

1,3

Comments

Suggested by Eq. (80) of (Maia and Mendez, 2008).

Links

Seiichi Manyama, Table of n, a(n) for n = 1..453

M. Maia and M. Mendez, On the arithmetic product of combinatorial species, Discr. Math., 308 (2008), 5407-5427.

Maple

with(numtheory);
f:=proc(n) local d; option remember;
if n=1 then 1
else add( ((n-1)!/(d!*((n-1)/d)!))*((n-1)/d)*f(d), d in divisors(n-1)); fi;
end;
[seq(f(n), n=1..40)];

Mathematica

f[n_] := Block[{m = n - 1}, Plus @@ Flatten[((m!/(#!*(m/#)!)) (m/#)*f@#) & /@ Divisors@m]]; f[1] = 1; Array[f, 25] (* Robert G. Wilson v, Dec 10 2017 *)

Crossrefs

Cf. A295577, A295583.

Sequence in context: A236056 A347616 A280116 * A054297 A325158 A079514

Adjacent sequences: A295575 A295576 A295577 * A295579 A295580 A295581

Keyword

nonn

Author

N. J. A. Sloane, Dec 09 2017

Status

approved