A295577 a(1)=1; thereafter, a(n+1) = Sum_{d divides n} (n!/(d!*(n/d)!))*a(d).

1, 1, 2, 3, 10, 11, 192, 193, 3554, 23715, 190036, 190037, 20813718, 20813719, 1690001240, 23484574041, 182792522842, 182792522843, 50810028382044, 50810028382045, 18982767399108446, 346748732389572447, 3022335531740638048, 3022335531740638049, 1128891498261322308450, 11900565139463395908451

Offset

1,3

Comments

It is possible that A092986 (Maia and Mendez, 2008, Table 1) is an erroneous version of this sequence.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..454

M. Maia and M. Mendez, On the arithmetic product of combinatorial species, Discr. Math., 308 (2008), 5407-5427. See Table 1.

Maple

with(numtheory);
f:=proc(n) local d; option remember;
if n=1 then 1
else add( ((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/#)!))*f@#) & /@ Divisors@ m]]; f[1] = 1; Array[f, 26] (* Robert G. Wilson v, Dec 10 2017 *)

Crossrefs

Cf. A092986, A295578, A295583.

Sequence in context: A193652 A345369 A092986 * A325256 A302388 A006092

Adjacent sequences: A295574 A295575 A295576 * A295578 A295579 A295580

Keyword

nonn

Author

N. J. A. Sloane, Dec 09 2017

Status

approved