A309171 a(n) = Product_{d|n} Stirling2(n,d).

1, 1, 1, 7, 1, 2790, 1, 216027, 3025, 21730275, 1, 143362465643243568744, 1, 404056132480, 500592722458920, 12056706465173227408551, 1, 99260615209905051640711424376160950, 1, 105138504356810366747790360523498652392500, 143413971571112402506500, 768149712982621155186

Offset: 1

Author

Ilya Gutkovskiy, Jul 15 2019

Keywords

• nonn

Crossrefs

Cf. A008277, A008578 (positions of 1's), A058808, A308037, A309169.

Programs

Magma

[(&*[StirlingSecond(n,d): d in Divisors(n)]): n in [1..30]]; // Vincenzo Librandi, Jul 16 2019

Mathematica

Table[Product[StirlingS2[n, d], {d, Divisors[n]}], {n, 1, 22}]

PARI

a(n) = my(d=divisors(n)); prod(k=1, #d, stirling(n, d[k], 2)); \\ Michel Marcus, Jul 16 2019