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

Offset

0,11

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.

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(PARI) { for (n=0, 100, p=1; x=n; until (x==0, p*=(x - 10*(x\10))!; x\=10); write("b061603.txt", n, " ", n!/p) ) } \\ Harry J. Smith, Jul 25 2009
(PARI) a(n) = my(d = digits(n)); n!/prod(k=1, #d, d[k]!); \\ Michel Marcus, Jul 02 2018

Crossrefs

Cf. A000142, A061602, A066459.

Sequence in context: A321846 A226889 A284207 * A153761 A133132 A228913

Adjacent sequences: A061600 A061601 A061602 * A061604 A061605 A061606

Keyword

nonn,base,easy

Author

Amarnath Murthy, May 19 2001

Extensions

Corrected and extended by Vladeta Jovovic, May 19 2001

Status

approved