A061603 a(n) = n! / {product of factorials of the digits of n}.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3628800, 39916800, 239500800, 1037836800, 3632428800, 10897286400, 29059430400, 70572902400, 158789030400, 335221286400, 1216451004088320000, 25545471085854720000, 281000181944401920000, 2154334728240414720000

Offset: 0

Author

Amarnath Murthy, May 19 2001

Keywords

• nonn
• base
• easy

Comments

It can be shown that the terms obtained by the above formula are positive integers using the fact that k! divides a product of k consecutive numbers.

Examples

			a(12) = (12!) / (1!*2!) = 239500800.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A000142, A061602, A066459.

Programs

Mathematica

Table[n!/Times@@(IntegerDigits[n]!),{n,0,30}] (* Harvey P. Dale, Jan 19 2017 *)

PARI

a(n) = my(d = digits(n)); n!/prod(k=1, #d, d[k]!); \\ Michel Marcus, Jul 02 2018

Formula

a(n) = A000142(n)/A066459(n). - Michel Marcus, Jul 02 2018

Extensions

Corrected and extended by Vladeta Jovovic, May 19 2001