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%I #13 Dec 07 2020 02:08:20
%S 1,10,1588,479632,181913856,78132541528,36324664278320,
%T 17841778519299678,9124496750611111054,4812920777714763364122,
%U 2601500672087054002816858,1434306387533099461310390376,803846503605741741601245431730,456755915371658053029595187998278
%N Number of 2*n-element subsets that can be chosen from {1,2,...,20*n} having element sum n*(20*n+1).
%C a(n) is the number of partitions of n*(20*n+1) into 2*n distinct parts <=20*n.
%H Alois P. Heinz, <a href="/A204466/b204466.txt">Table of n, a(n) for n = 0..30</a>
%e a(1) = 10 because there are 10 2-element subsets that can be chosen from {1,2,...,20} having element sum 21: {1,20}, {2,19}, {3,18}, {4,17}, {5,16}, {6,15}, {7,14}, {8,13}, {9,12}, {10,11}.
%p b:= proc(n, i, t) option remember;
%p `if`(i<t or n<t*(t+1)/2 or n>t*(2*i-t+1)/2, 0,
%p `if`(n=0, 1, b(n, i-1, t) +`if`(n<i, 0, b(n-i, i-1, t-1))))
%p end:
%p a:= n-> b(n*(20*n+1), 20*n, 2*n):
%p seq(a(n), n=0..10);
%t b[n_, i_, t_] /; i<t || n<t(t+1)/2 || n>t(2i-t+1)/2 = 0; b[0, _, _] = 1;
%t b[n_, i_, t_] := b[n, i, t] = b[n, i-1, t] + If[n<i, 0, b[n-i, i-1, t-1]];
%t a[n_] := b[n(20n+1), 20n, 2n];
%t a /@ Range[0, 10] (* _Jean-François Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)
%Y Bisection of row n=10 of A204459.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Jan 18 2012
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