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Number of partitions of 2^n into powers of 2 less than or equal to 128.
2

%I #9 Jun 13 2015 00:54:12

%S 1,2,4,10,36,202,1828,27338,692003,29559717,1933411785,169368653201,

%T 17695666168609,2038699559609921,247324139826203777,

%U 30811717563505088769,3890604470232727499265,494612931489164269609985,63094694253683687355107329

%N Number of partitions of 2^n into powers of 2 less than or equal to 128.

%H Alois P. Heinz, <a href="/A210776/b210776.txt">Table of n, a(n) for n = 0..150</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (255, -21590, 777240, -12850368, 99486720, -353730560, 534773760, -268435456).

%F G.f.: (4009754624*x^13 -4990304256*x^12 +1018234880*x^11 -57698752*x^10 -28134460*x^9 -42258923*x^8 -120814102*x^7 +199113750*x^6 -76688022*x^5 +11379734*x^4-735070*x^3+21084*x^2-253*x+1)/Product_{j=0..7} (2^j*x-1).

%F a(n) = [x^2^(n-1)] 1/(1-x) * 1/Product_{j=0..6} (1-x^(2^j)) for n>0.

%p gf:= (1 +(-253 +(21084 +(-735070 +(11379734 +(-76688022 +(199113750 +(-120814102 +(-42258923 +(-28134460 +(-57698752+(1018234880 +(-4990304256 +4009754624*x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x)/ mul(2^j*x-1, j=0..7): a:= n-> coeff(series(gf, x, n+1), x, n): seq(a(n), n=0..20);

%Y Column k=7 of A152977.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Mar 26 2012