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A210774 Number of partitions of 2^n into powers of 2 less than or equal to 32.

%I A210774 #9 Jun 13 2015 00:54:12
%S A210774 1,2,4,10,36,202,1827,25509,497097,12070289,333620001,9898583617,
%T A210774 304816671873,9567029991681,303182221750785,9654673365689345,
%U A210774 308196987575257089,9850278328626941953,315016627560700387329,10077456621734453460993,322429412555504845881345
%N A210774 Number of partitions of 2^n into powers of 2 less than or equal to 32.
%H A210774 Alois P. Heinz, <a href="/A210774/b210774.txt">Table of n, a(n) for n = 0..200</a>
%H A210774 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (63, -1302, 11160, -41664, 64512, -32768).
%F A210774 G.f.: -(2048*x^9 -320*x^8 +4220*x^7 +5227*x^6 +14870*x^5 -23958*x^4 +8798*x^3 -1180*x^2 +61*x -1) / Product_{j=0..5} (2^j*x-1).
%F A210774 a(n) = [x^2^(n-1)] 1/(1-x) * 1/Product_{j=0..4} (1-x^(2^j)) for n>0.
%p A210774 a:= n-> `if`(n<5, [1, 2, 4, 10, 36][n+1], (Matrix(6, (i, j)-> `if`(i=j-1, 1, `if`(i=6, [-32768, 64512, -41664, 11160, -1302, 63][j], 0)))^(n-5). <<202, 1827, 25509, 497097, 12070289, 333620001>>)[1,1]): seq(a(n), n=0..20);
%Y A210774 Column k=5 of A152977.
%K A210774 nonn,easy
%O A210774 0,2
%A A210774 _Alois P. Heinz_, Mar 26 2012