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A378959 Sum, in base 10, of the permutations of the digits of n, written in base 2.

%I A378959 #27 Jun 11 2025 14:58:27
%S A378959 0,1,3,3,7,14,14,7,15,45,45,45,45,45,45,15,31,124,124,186,124,186,186,
%T A378959 124,124,186,186,124,186,124,124,31,63,315,315,630,315,630,630,630,
%U A378959 315,630,630,630,630,630,630,315,315,630,630,630,630,630,630,315,630
%N A378959 Sum, in base 10, of the permutations of the digits of n, written in base 2.
%C A378959 Fixed points are in A000225.
%H A378959 Alois P. Heinz, <a href="/A378959/b378959.txt">Table of n, a(n) for n = 0..16384</a>
%F A378959 a(n) = A003817(n) * A090706(n). - _Alois P. Heinz_, Dec 12 2024
%e A378959 a(5) = 14 because 5 in base 2 is 101 and the permutations of the digits are 101, 110, 011 that correspond to 5, 6, 3 and 5 + 6 + 3 = 14.
%p A378959 a:= proc(n) local k, l;
%p A378959       l:= convert(n, base, 2); k:= nops(l);
%p A378959       binomial(k-1, add(i, i=l)-1)*(2^k-1)
%p A378959     end:
%p A378959 seq(a(n), n=0..56);  # _Alois P. Heinz_, Dec 12 2024
%t A378959 A378959[n_] := (2^# - 1)*Binomial[# - 1, DigitCount[n, 2, 0]] & [BitLength[n]];
%t A378959 Array[A378959, 100, 0] (* _Paolo Xausa_, Jan 29 2025 *)
%Y A378959 Cf. A000120, A000225, A003817, A090706, A134346.
%K A378959 nonn,base
%O A378959 0,3
%A A378959 _Paolo P. Lava_, Dec 12 2024