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a(n) = Sum_{j=0..n} n^wt(j), where wt = A000120.
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%I #17 Mar 06 2023 19:34:57

%S 1,2,5,16,29,66,127,512,737,1090,1541,3312,4369,7658,12209,65536,

%T 83537,105282,130987,167600,203701,254122,313259,649728,766201,912626,

%U 1079027,1778896,2071469,3081570,4329151,33554432,39135425,45436546,52524221,60511536

%N a(n) = Sum_{j=0..n} n^wt(j), where wt = A000120.

%H Alois P. Heinz, <a href="/A361257/b361257.txt">Table of n, a(n) for n = 0..16382</a>

%F a(n) = Sum_{j=0..n} n^wt(j), where wt = A000120.

%F a(n) = Sum_{k>=0} n^k * A360189(n,k).

%F a(n) mod 2 = A059841(n).

%F a(2^n-1) = 2^(n^2) = A002416(n).

%p b:= proc(n) option remember; `if`(n<0, 0,

%p b(n-1)+x^add(i, i=Bits[Split](n)))

%p end:

%p a:= n-> subs(x=n, b(n)):

%p seq(a(n), n=0..37);

%o (Python)

%o def A361257(n): return sum([n**j.bit_count() for j in range(0,n+1)])

%o print(list(A361257(n) for n in range(0,37))) # _Dumitru Damian_, Mar 06 2023

%o (Python)

%o from collections import Counter

%o def A361257(n): return sum(j*n**i for i, j in Counter(j.bit_count() for j in range(n+1)).items()) # _Chai Wah Wu_, Mar 06 2023

%Y Cf. A000120, A002416, A059841, A360189.

%K nonn,base

%O 0,2

%A _Alois P. Heinz_, Mar 06 2023