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

%I A384955 #23 Jun 15 2025 20:54:11
%S A384955 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,
%T A384955 1,4,10,20,35,56,84,120,165,220,1,5,15,35,70,126,210,330,495,715,1,6,
%U A384955 21,56,126,252,462,792,1287,2002,1,7,28,84,210,462,924,1716,3003,5005
%N A384955 a(n) is the multinomial coefficient of the digits of n.
%H A384955 Stefano Spezia, <a href="/A384955/b384955.txt">Table of n, a(n) for n = 0..10000</a>
%F A384955 a(n) = A269221(n)/A066459(n).
%F A384955 a(n) = 1 iff n is equal to 0 or has only one nonzero digit (cf. A037124).
%F A384955 Conjecture: a(n) = n iff n = 1 or n = 1512.
%e A384955 a(35) = (3+5)!/(3!*5!) = 40320/(6*120) = 56;
%e A384955 a(1512) = (1+5+1+2)!/(1!*5!*1!*2!) = 362880/(120*2) = 1512.
%p A384955 a:= n-> (l-> combinat[multinomial](add(i,i=l), l[]))(convert(n, base, 10)):
%p A384955 seq(a(n), n=0..69);  # _Alois P. Heinz_, Jun 15 2025
%t A384955 a[n_]:=Multinomial @@IntegerDigits[n]; Array[a,70,0]
%o A384955 (Python)
%o A384955 from math import factorial, prod
%o A384955 def a(n): return factorial(sum(digits:=list(map(int, str(n))))) // prod(factorial(x) for x in digits)
%o A384955 print([a(n) for n in range(70)]) # _David Radcliffe_, Jun 15 2025
%Y A384955 Cf. A037124, A066459, A093659, A269221.
%K A384955 nonn,base,easy,look
%O A384955 0,12
%A A384955 _Stefano Spezia_, Jun 13 2025