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

1, 10, 65, 330, 1430, 5510, 19395, 63440, 195250, 570570, 1594315, 4283270, 11113440, 27949580, 68340360, 162880080, 379227010, 864153940, 1930443705, 4233724000, 9127235430, 19364099520, 40470110005, 83395632580, 169581447000, 340533848010

Offset: 0

Author

N. J. A. Sloane, Nov 13 2009

Keywords

• nonn

Examples

			G.f.: 1+10*q^24+65*q^48+330*q^72+1430*q^96+5510*q^120+19395*q^144+...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Watson, G. N., Ramanujans Vermutung ueber Zerfaellungsanzahlen. J. Reine Angew. Math. (Crelle), 179 (1938), 97-128. See the expression C^2/B^10.

Crossrefs

Cf. A160459, A277212.

Programs

Maple

read format;
M1:=1200:
fm:=mul(1-x^n,n=1..M1):
A:=x^(1/5)*subs(x=x^(24/5),fm):
B:=x*subs(x=x^24,fm):
C:=x^5*subs(x=x^120,fm):
t1:=C^2/B^10;
t2:=series(t1,x,M1);
t3:=subs(x=y^(1/24),t2);
t4:=series(t3,y,M1/24);
t5:=seriestolist(t4); # A160458

PARI

x='x+O('x^66); Vec((eta(x^5)/eta(x)^5)^2) \\ Joerg Arndt, Nov 27 2016

Formula

See Maple code for formula.

a(n) = Sum_{k=0..n} A277212(k)*A277212(n-k). - Seiichi Manyama, Nov 27 2016