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A061603
a(n) = n! / {product of factorials of the digits of n}.
2
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
0,11
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
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
KEYWORD
nonn,base,easy
AUTHOR
Amarnath Murthy, May 19 2001
EXTENSIONS
Corrected and extended by Vladeta Jovovic, May 19 2001
STATUS
approved