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

0,12

Links

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

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.

Example

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

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]

Prog

(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

Crossrefs

Cf. A037124, A066459, A093659, A269221.

Sequence in context: A274206 A214949 A067453 * A203814 A381963 A373211

Adjacent sequences: A384952 A384953 A384954 * A384956 A384957 A384958

Keyword

nonn,base,easy,look

Author

Stefano Spezia, Jun 13 2025

Status

approved