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

1, 1, 2, 9, 4, 25, 36, 343, 8, 81, 100, 1331, 144, 2197, 2744, 50625, 16, 289, 324, 6859, 400, 9261, 10648, 279841, 576, 15625, 17576, 531441, 21952, 707281, 810000, 28629151, 32, 1089, 1156, 42875, 1296, 50653, 54872, 2313441, 1600, 68921, 74088, 3418801, 85184, 4100625, 4477456, 229345007, 2304

Offset: 0

Author

Ilya Gutkovskiy, Apr 08 2018

Keywords

• nonn

Examples

			+---+-----+---+----------+
| n | bin.|1's|   a(n)   |
+---+-----+---+----------+
| 0 |   0 | 0 | 0^0 =  1 |
| 1 |   1 | 1 | 1^1 =  1 |
| 2 |  10 | 1 | 2^1 =  2 |
| 3 |  11 | 2 | 3^2 =  9 |
| 4 | 100 | 1 | 4^1 =  4 |
| 5 | 101 | 2 | 5^2 = 25 |
| 6 | 110 | 2 | 6^2 = 36 |
+---+-----+---+----------+
bin. - n written in base 2;
1's - number of 1's in binary expansion of n.
		

Links

• Index entries for sequences related to cellular automata
• Index entries for sequences related to binary expansion of n

Crossrefs

Main diagonal of A256140.

Cf. A000120, A001316, A048883, A102376, A245788.

Programs

Mathematica

Table[SeriesCoefficient[Product[(1 + n x^(2^k)), {k, 0, n}], {x, 0, n}], {n, 0, 48}]
Join[{1}, Table[n^DigitCount[n, 2, 1], {n, 48}]]

PARI

a(n) = n^hammingweight(n); \\ Altug Alkan, Apr 08 2018

Formula

a(n) = n^A000120(n).

a(n) = A256140(n,n).

a(2^k) = 2^k.

a(2^k-1) = (2^k - 1)^k.