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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

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

Cf. A160459, A277212.

Sequence in context: A059598 A327388 A133715 * A023009 A169797 A073381

Adjacent sequences:  A160455 A160456 A160457 * A160459 A160460 A160461

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 13 2009

STATUS

approved

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Last modified July 8 17:40 EDT 2020. Contains 335524 sequences. (Running on oeis4.)