A282941 - OEIS

%I #16 Feb 27 2017 07:28:49

%S 1,41,-176,98,322,-181,-140,-489,112,889,14,-560,125,154,756,-1317,

%T -1778,1554,-1218,2688,1764,-980,71,-1575,14,-1638,-419,56,-1988,

%U -2716,6223,6860,1302,-700,-3416,-4733,-2548,-4725,3836,1106,2631,5096,-5656,2660,-7875

%N a(n) = A000730(7*n).

%D G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 191.

%H Seiichi Manyama, <a href="/A282941/b282941.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{n>=1} (1 - q^n)^8/(1 - q^(7*n)) + 49*q*(Product_{n>=1} (1 - q^n)^4*(1 - q^(7*n))^3).

%F a(n) = (-1)^j mod 7 if n = j*(3*j - 1)/2 for all j in Z; otherwise a(n) = 0 mod 7.

%F a(n) = A282942(n) mod 49.

%e G.f.: 1 + 41*q - 176*q^2 + 98*q^3 + 322*q^4 - 181*q^5 - 140*q^6 - 489*q^7 + ...

%Y Cf. A000730, A116916, A282937, A282942.

%K sign

%O 0,2

%A _Seiichi Manyama_, Feb 25 2017