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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 über Zerfällungsanzahlen, 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.)