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A240143 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 7.

%I A240143 #8 Apr 03 2014 09:33:35
%S A240143 1,0,1,0,2,0,3,0,5,0,7,0,11,0,15,0,21,1,28,2,38,4,49,7,65,12,82,19,
%T A240143 105,30,131,45,164,67,201,96,248,136,301,188,366,258,441,347,531,463,
%U A240143 635,609,761,795,907,1025,1082,1313,1289,1665,1537,2099,1831,2624
%N A240143 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 7.
%C A240143 With offset 56 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -7.
%H A240143 Alois P. Heinz, <a href="/A240143/b240143.txt">Table of n, a(n) for n = 49..1000</a>
%F A240143 a(n) = [x^n y^7] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).
%e A240143 a(59) = 7: [23,11,9,7,5,3,1], [21,13,9,7,5,3,1], [19,15,9,7,5,3,1], [19,13,11,7,5,3,1], [17,15,11,7,5,3,1], [17,13,11,9,5,3,1], [15,13,11,9,7,3,1].
%e A240143 a(70) = 4: [19,13,11,9,7,5,3,2,1], [17,15,11,9,7,5,3,2,1], [17,13,11,9,7,5,4,3,1], [15,13,11,9,7,6,5,3,1].
%p A240143 b:= proc(n, i, t) option remember; `if`(n>i*(i+1)/2 or
%p A240143       abs(t)>n, 0, `if`(n=0, 1, b(n, i-1, t)+
%p A240143       `if`(i>n, 0, b(n-i, i-1, t+(2*irem(i, 2)-1)))))
%p A240143     end:
%p A240143 a:= n-> b(n$2, -7):
%p A240143 seq(a(n), n=49..120);
%Y A240143 Column k=7 of A240021.
%K A240143 nonn
%O A240143 49,5
%A A240143 _Alois P. Heinz_, Apr 02 2014