A301702 - OEIS

%I #10 Mar 27 2018 17:35:21

%S 1,1,5,19,89,401,1877,8821,41969,200899,967605,4681491,22739705,

%T 110816343,541561333,2653061819,13024808161,64063300481,315624211781,

%U 1557318893473,7694243895289,38060959885345,188482408625373,934323819631893,4635781966972721,23020536772620401

%N a(n) = [x^n] Product_{k>=0} 1/(1 - x^(2^k))^n.

%C Number of binary partitions of n into parts of n kinds.

%H Vaclav Kotesovec, <a href="/A301702/b301702.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%t Table[SeriesCoefficient[Product[1/(1 - x^(2^k))^n, {k, 0, n}], {x, 0, n}], {n, 0, 25}]

%t Table[SeriesCoefficient[Product[(1 + x^(2^k))^(n (k + 1)), {k, 0, n}], {x, 0, n}], {n, 0, 25}]

%Y Cf. A000123, A008485, A018819, A038712, A171238.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 25 2018