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A240146 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 10.

%I A240146 #8 Apr 03 2014 09:34:15
%S A240146 1,0,1,0,2,0,3,0,5,0,7,0,11,0,15,0,22,0,30,0,42,0,55,1,75,2,97,4,128,
%T A240146 7,164,12,212,19,267,30,340,45,423,67,530,97,653,139,807,195,984,271,
%U A240146 1204,370,1456,501,1763,670,2117,889,2543,1167,3032,1522,3618
%N A240146 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 10.
%C A240146 With offset 110 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -10.
%H A240146 Alois P. Heinz, <a href="/A240146/b240146.txt">Table of n, a(n) for n = 100..1000</a>
%F A240146 a(n) = [x^n y^10] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).
%e A240146 a(104) = 2: [23,17,15,13,11,9,7,5,3,1], [21,19,15,13,11,9,7,5,3,1].
%e A240146 a(125) = 2: [23,19,17,15,13,11,9,7,5,3,2,1], [21,19,17,15,13,11,9,7,5,4,3,1].
%p A240146 b:= proc(n, i, t) option remember; `if`(n>i*(i+1)/2 or
%p A240146       abs(t)>n, 0, `if`(n=0, 1, b(n, i-1, t)+
%p A240146       `if`(i>n, 0, b(n-i, i-1, t+(2*irem(i, 2)-1)))))
%p A240146     end:
%p A240146 a:= n-> b(n$2, -10):
%p A240146 seq(a(n), n=100..160);
%Y A240146 Column k=10 of A240021.
%K A240146 nonn
%O A240146 100,5
%A A240146 _Alois P. Heinz_, Apr 02 2014