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A160458
Coefficients in the expansion of C^2/B^10, in Watson's notation of page 106.
8
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
0,2
LINKS
Watson, G. N., Ramanujans Vermutung ueber Zerfaellungsanzahlen. J. Reine Angew. Math. (Crelle), 179 (1938), 97-128. See the expression C^2/B^10.
FORMULA
See Maple code for formula.
a(n) = Sum_{k=0..n} A277212(k)*A277212(n-k). - Seiichi Manyama, Nov 27 2016
EXAMPLE
G.f.: 1+10*q^24+65*q^48+330*q^72+1430*q^96+5510*q^120+19395*q^144+...
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
PROG
(PARI) x='x+O('x^66); Vec((eta(x^5)/eta(x)^5)^2) \\ Joerg Arndt, Nov 27 2016
CROSSREFS
Sequence in context: A327388 A341387 A133715 * A023009 A169797 A073381
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 13 2009
STATUS
approved