A384955 a(n) is the multinomial coefficient of the digits of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1, 6, 21, 56, 126, 252, 462, 792, 1287, 2002, 1, 7, 28, 84, 210, 462, 924, 1716, 3003, 5005

Offset: 0

Author

Stefano Spezia, Jun 13 2025

Keywords

• nonn
• base
• easy
• look

Examples

			a(35) = (3+5)!/(3!*5!) = 40320/(6*120) = 56;
a(1512) = (1+5+1+2)!/(1!*5!*1!*2!) = 362880/(120*2) = 1512.
		

Links

• Stefano Spezia, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A037124, A066459, A093659, A269221.

Programs

Maple

a:= n-> (l-> combinat[multinomial](add(i,i=l), l[]))(convert(n, base, 10)):
seq(a(n), n=0..69);  # Alois P. Heinz, Jun 15 2025

Mathematica

a[n_]:=Multinomial @@IntegerDigits[n]; Array[a,70,0]

Python

from math import factorial, prod
def a(n): return factorial(sum(digits:=list(map(int, str(n))))) // prod(factorial(x) for x in digits)
print([a(n) for n in range(70)]) # David Radcliffe, Jun 15 2025

Formula

a(n) = A269221(n)/A066459(n).

a(n) = 1 iff n is equal to 0 or has only one nonzero digit (cf. A037124).

Conjecture: a(n) = n iff n = 1 or n = 1512.