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A160458 Coefficients in the expansion of C^2/B^10, in Watson's notation of page 106.

%I A160458 #19 Aug 11 2025 06:54:41
%S A160458 1,10,65,330,1430,5510,19395,63440,195250,570570,1594315,4283270,
%T A160458 11113440,27949580,68340360,162880080,379227010,864153940,1930443705,
%U A160458 4233724000,9127235430,19364099520,40470110005,83395632580,169581447000,340533848010
%N A160458 Coefficients in the expansion of C^2/B^10, in Watson's notation of page 106.
%H A160458 Seiichi Manyama, <a href="/A160458/b160458.txt">Table of n, a(n) for n = 0..1000</a>
%H A160458 Watson, G. N., <a href="https://gdz.sub.uni-goettingen.de/id/PPN243919689_0179">Ramanujans Vermutung ueber Zerfaellungsanzahlen.</a> J. Reine Angew. Math. (Crelle), 179 (1938), 97-128. See the expression C^2/B^10.
%F A160458 See Maple code for formula.
%F A160458 a(n) = Sum_{k=0..n} A277212(k)*A277212(n-k). - _Seiichi Manyama_, Nov 27 2016
%e A160458 G.f.: 1+10*q^24+65*q^48+330*q^72+1430*q^96+5510*q^120+19395*q^144+...
%p A160458 read format;
%p A160458 M1:=1200:
%p A160458 fm:=mul(1-x^n,n=1..M1):
%p A160458 A:=x^(1/5)*subs(x=x^(24/5),fm):
%p A160458 B:=x*subs(x=x^24,fm):
%p A160458 C:=x^5*subs(x=x^120,fm):
%p A160458 t1:=C^2/B^10;
%p A160458 t2:=series(t1,x,M1);
%p A160458 t3:=subs(x=y^(1/24),t2);
%p A160458 t4:=series(t3,y,M1/24);
%p A160458 t5:=seriestolist(t4); # A160458
%o A160458 (PARI) x='x+O('x^66); Vec((eta(x^5)/eta(x)^5)^2) \\ _Joerg Arndt_, Nov 27 2016
%Y A160458 Cf. A160459, A277212.
%K A160458 nonn
%O A160458 0,2
%A A160458 _N. J. A. Sloane_, Nov 13 2009