%I #6 Apr 09 2018 22:33:35
%S 1,1,2,9,4,25,36,343,8,81,100,1331,144,2197,2744,50625,16,289,324,
%T 6859,400,9261,10648,279841,576,15625,17576,531441,21952,707281,
%U 810000,28629151,32,1089,1156,42875,1296,50653,54872,2313441,1600,68921,74088,3418801,85184,4100625,4477456,229345007,2304
%N a(n) = [x^n] Product_{k>=0} (1 + n*x^(2^k)).
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(n) = n^A000120(n).
%F a(n) = A256140(n,n).
%F a(2^k) = 2^k.
%F a(2^k-1) = (2^k - 1)^k.
%e +---+-----+---+----------+
%e | n | bin.|1's| a(n) |
%e +---+-----+---+----------+
%e | 0 | 0 | 0 | 0^0 = 1 |
%e | 1 | 1 | 1 | 1^1 = 1 |
%e | 2 | 10 | 1 | 2^1 = 2 |
%e | 3 | 11 | 2 | 3^2 = 9 |
%e | 4 | 100 | 1 | 4^1 = 4 |
%e | 5 | 101 | 2 | 5^2 = 25 |
%e | 6 | 110 | 2 | 6^2 = 36 |
%e +---+-----+---+----------+
%e bin. - n written in base 2;
%e 1's - number of 1's in binary expansion of n.
%t Table[SeriesCoefficient[Product[(1 + n x^(2^k)), {k, 0, n}], {x, 0, n}], {n, 0, 48}]
%t Join[{1}, Table[n^DigitCount[n, 2, 1], {n, 48}]]
%o (PARI) a(n) = n^hammingweight(n); \\ _Altug Alkan_, Apr 08 2018
%Y Main diagonal of A256140.
%Y Cf. A000120, A001316, A048883, A102376, A245788.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Apr 08 2018