A300659 Product of digits of n!.

1, 1, 2, 6, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Jaroslav Krizek, Jun 05 2018

Keywords

• nonn
• base
• easy
• changed

Comments

Also multiplicative digital root of n!.

Decimal expansion of 2817/25000. - Eric Chen, Jun 06 2018

Links

• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A000142, A007954, A031347, A067067, A086358, A004152.

Programs

Magma

[&*Intseq(Factorial(n)): n in [0..100]];

Mathematica

Array[Times @@ IntegerDigits[#!] &, 105] (* Michael De Vlieger, Jun 06 2018 *)

PARI

a(n) = my(d=digits(n!)); prod(k=1, #d, d[k]); \\ Michel Marcus, Jun 05 2018

Formula

G.f.: 1 + x + 2*x^2 + 6*x^3 + 8*x^4.

a(n) = 0 for n >= 5.

a(n) = A031347(A000142(n)).

a(n) = A007954(A000142(n)). - Eric Chen, Jun 06 2018