cp's OEIS Frontend

A302451 a(n) = [x^n] Product_{k>=0} (1 + n*x^(2^k)).

%I A302451 #6 Apr 09 2018 22:33:35
%S A302451 1,1,2,9,4,25,36,343,8,81,100,1331,144,2197,2744,50625,16,289,324,
%T A302451 6859,400,9261,10648,279841,576,15625,17576,531441,21952,707281,
%U A302451 810000,28629151,32,1089,1156,42875,1296,50653,54872,2313441,1600,68921,74088,3418801,85184,4100625,4477456,229345007,2304
%N A302451 a(n) = [x^n] Product_{k>=0} (1 + n*x^(2^k)).
%H A302451 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A302451 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A302451 a(n) = n^A000120(n).
%F A302451 a(n) = A256140(n,n).
%F A302451 a(2^k) = 2^k.
%F A302451 a(2^k-1) = (2^k - 1)^k.
%e A302451 +---+-----+---+----------+
%e A302451 | n | bin.|1's|   a(n)   |
%e A302451 +---+-----+---+----------+
%e A302451 | 0 |   0 | 0 | 0^0 =  1 |
%e A302451 | 1 |   1 | 1 | 1^1 =  1 |
%e A302451 | 2 |  10 | 1 | 2^1 =  2 |
%e A302451 | 3 |  11 | 2 | 3^2 =  9 |
%e A302451 | 4 | 100 | 1 | 4^1 =  4 |
%e A302451 | 5 | 101 | 2 | 5^2 = 25 |
%e A302451 | 6 | 110 | 2 | 6^2 = 36 |
%e A302451 +---+-----+---+----------+
%e A302451 bin. - n written in base 2;
%e A302451 1's - number of 1's in binary expansion of n.
%t A302451 Table[SeriesCoefficient[Product[(1 + n x^(2^k)), {k, 0, n}], {x, 0, n}], {n, 0, 48}]
%t A302451 Join[{1}, Table[n^DigitCount[n, 2, 1], {n, 48}]]
%o A302451 (PARI) a(n) = n^hammingweight(n); \\ _Altug Alkan_, Apr 08 2018
%Y A302451 Main diagonal of A256140.
%Y A302451 Cf. A000120, A001316, A048883, A102376, A245788.
%K A302451 nonn
%O A302451 0,3
%A A302451 _Ilya Gutkovskiy_, Apr 08 2018