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Coefficients in the expansion of B^7/C, in Watson's notation of page 118.
4

%I #12 Jan 04 2019 04:21:43

%S 1,-7,14,7,-49,21,35,42,-56,-119,105,-70,147,147,-133,-168,-231,252,

%T -154,315,441,7,-644,-574,595,-679,735,574,196,-406,-840,840,-1470,

%U 854,1260,21,-1617,-966,1575,-1176,1785,1470,35,-1974,-2058,1533,-1988,1932,2387,-301,-2170,-2016,3087,-2422

%N Coefficients in the expansion of B^7/C, in Watson's notation of page 118.

%H Seiichi Manyama, <a href="/A160534/b160534.txt">Table of n, a(n) for n = 0..1000</a>

%H Watson, G. N., <a href="http://www.digizeitschriften.de/dms/resolveppn/?PID=GDZPPN002174499">Ramanujans Vermutung ueber Zerfaellungsanzahlen.</a> J. Reine Angew. Math. (Crelle), 179 (1938), 97-128.

%F See Maple code in A160525 for formula.

%F Euler transform of period 7 sequence [ -7, -7, -7, -7, -7, -7, -6, ...]. - _Alois P. Heinz_, Jan 07 2017

%e 1-7*x^24+14*x^48+7*x^72-49*x^96+21*x^120+35*x^144+42*x^168-...

%p with(numtheory):

%p a:= proc(n) option remember; `if`(n=0, 1, add(add(d*

%p `if`(irem(d, 7)=0, -6, -7), d=divisors(j))*a(n-j), j=1..n)/n)

%p end:

%p seq(a(n), n=0..70); # _Alois P. Heinz_, Jan 07 2017

%t a[n_] := a[n] = If[n==0, 1, Sum[DivisorSum[j, #*If[Mod[#, 7]==0, -6, -7]&]* a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 70}] (* _Jean-François Alcover_, Mar 13 2017, after _Alois P. Heinz_ *)

%K sign

%O 0,2

%A _N. J. A. Sloane_, Nov 14 2009