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A160539 Coefficients in the expansion of C/B^7, in Watson's notation of page 118. 6
1, 7, 35, 140, 490, 1547, 4522, 12404, 32298, 80430, 192759, 446656, 1004598, 2199953, 4703104, 9836820, 20167210, 40593651, 80335164, 156503088, 300457906, 568992893, 1063818868, 1965178600, 3589328246, 6485976525, 11602141453, 20555544212, 36087448852 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Watson's C and B are (essentially) defined as C=prod(n>=1, 1-q^(7*n)) and B=prod(n>=1, 1-q^n). [Joerg Arndt, Jul 30 2011]

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

G. N. Watson, Ramanujans Vermutung √ľber Zerf√§llungsanzahlen, J. Reine Angew.Math. (Crelle), 179 (1938), 97-128.

FORMULA

G.f.: E7/E1^7 where E1=P(q), E7=P(q^7) and P(q)=prod(n>=1, 1-q^n). [Joerg Arndt, Jul 30 2011]

G.f.: exp(sum(n>=1, (sigma(7*n)-sigma(n))*x^n/n ) ). [Joerg Arndt, Jul 30 2011]

See also Maple code in A160525 for formula.

a(n) ~ 2^(5/4) * exp(4*Pi*sqrt(2*n/7)) / (7^(9/4) * n^(9/4)). - Vaclav Kotesovec, Nov 10 2016

EXAMPLE

1+7*x^24+35*x^48+140*x^72+490*x^96+1547*x^120+4522*x^144+...

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1 - x^(7*k))/(1 - x^k)^7, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2016 *)

PROG

(PARI) N=66; x='x+O('x^N);

gf=eta(x^7)/eta(x)^7;

Vec(gf) /* Joerg Arndt, Jul 30 2011 */

CROSSREFS

Sequence in context: A001941 A320050 A160460 * A023006 A001875 A169794

Adjacent sequences:  A160536 A160537 A160538 * A160540 A160541 A160542

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 14 2009

STATUS

approved

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Last modified May 26 13:05 EDT 2019. Contains 323586 sequences. (Running on oeis4.)