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A210778 Number of partitions of 2^n into powers of 2 less than or equal to 512.

%I A210778 #9 Jun 13 2015 00:54:13
%S A210778 1,2,4,10,36,202,1828,27338,692004,30251722,2320518947,314039061413,
%T A210778 69808185542089,22148021690928529,8756818568093328161,
%U A210778 3918553907116206319169,1872922535299778812595329,926165546297497921388714241,465979162430464375966575440385
%N A210778 Number of partitions of 2^n into powers of 2 less than or equal to 512.
%H A210778 Alois P. Heinz, <a href="/A210778/b210778.txt">Table of n, a(n) for n = 0..120</a>
%H A210778 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1023, -348502, 50781720, -3439615168, 111842970624, -1761082966016, 13312123207680, -46775146643456, 70300024700928, -35184372088832).
%F A210778 G.f.: (-537373113935986688*x^17 +691978531999055872*x^16 -160490503232552960*x^15 +5811316119175168*x^14 +75591601244160*x^13 -4465138103744*x^12 -3652534938428*x^11 -5517732454379*x^10 -15802918567958*x^9 +26190980411414*x^8 -10204692593686*x^7 +1550660009494*x^6 -105163418774*x^5 +3339435542*x^4 -50088798*x^3 +346460*x^2 -1021*x+1) / Product_{j=0..9} (2^j*x-1).
%F A210778 a(n) = [x^2^(n-1)] 1/(1-x) * 1/Product_{j=0..8} (1-x^(2^j)) for n>0.
%p A210778 gf:= (1+ (-1021 +(346460 +(-50088798 +(3339435542 +(-105163418774 +(1550660009494 +(-10204692593686 +(26190980411414 +(-15802918567958 +(-5517732454379 +(-3652534938428 +(-4465138103744 +(75591601244160 +(5811316119175168 +(-160490503232552960 +(691978531999055872 -537373113935986688*x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x)/ mul(2^j*x-1, j=0..9): a:= n-> coeff(series(gf, x, n+1), x, n): seq(a(n), n=0..20);
%Y A210778 Column k=9 of A152977.
%K A210778 nonn,easy
%O A210778 0,2
%A A210778 _Alois P. Heinz_, Mar 26 2012