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A240144 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 8.

%I A240144 #8 Apr 03 2014 09:33:54
%S A240144 1,0,1,0,2,0,3,0,5,0,7,0,11,0,15,0,22,0,29,1,40,2,52,4,70,7,89,12,116,
%T A240144 19,146,30,186,45,230,67,288,97,352,138,434,192,526,265,640,359,769,
%U A240144 482,928,639,1107,840,1325,1092,1574,1410,1874,1803,2218,2291
%N A240144 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 8.
%C A240144 With offset 72 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -8.
%H A240144 Alois P. Heinz, <a href="/A240144/b240144.txt">Table of n, a(n) for n = 64..1000</a>
%F A240144 a(n) = [x^n y^8] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).
%e A240144 a(70) = 3: [21,13,11,9,7,5,3,1], [19,15,11,9,7,5,3,1], [17,15,13,9,7,5,3,1].
%e A240144 a(85) = 2: [19,15,13,11,9,7,5,3,2,1], [17,15,13,11,9,7,5,4,3,1].
%p A240144 b:= proc(n, i, t) option remember; `if`(n>i*(i+1)/2 or
%p A240144       abs(t)>n, 0, `if`(n=0, 1, b(n, i-1, t)+
%p A240144       `if`(i>n, 0, b(n-i, i-1, t+(2*irem(i, 2)-1)))))
%p A240144     end:
%p A240144 a:= n-> b(n$2, -8):
%p A240144 seq(a(n), n=64..130);
%Y A240144 Column k=8 of A240021.
%K A240144 nonn
%O A240144 64,5
%A A240144 _Alois P. Heinz_, Apr 02 2014