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A204464 Number of 2*n-element subsets that can be chosen from {1,2,...,16*n} having element sum n*(16*n+1).

%I A204464 #11 Dec 07 2020 02:08:05
%S A204464 1,8,790,148718,35154340,9408671330,2725410001024,834014033203632,
%T A204464 265724127467961324,87318355216835049968,29402690636348418710858,
%U A204464 10098693807141197229592054,3525753285145412581617963136,1248001014165722671454730108968,446964111600452023289482445527716
%N A204464 Number of 2*n-element subsets that can be chosen from {1,2,...,16*n} having element sum n*(16*n+1).
%C A204464 a(n) is the number of partitions of n*(16*n+1) into 2*n distinct parts <=16*n.
%e A204464 a(1) = 8 because there are 8 2-element subsets that can be chosen from {1,2,...,16} having element sum 17: {1,16}, {2,15}, {3,14}, {4,13}, {5,12}, {6,11}, {7,10}, {8,9}.
%p A204464 b:= proc(n, i, t) option remember;
%p A204464       `if`(i<t or n<t*(t+1)/2 or n>t*(2*i-t+1)/2, 0,
%p A204464       `if`(n=0, 1, b(n, i-1, t) +`if`(n<i, 0, b(n-i, i-1, t-1))))
%p A204464     end:
%p A204464 a:= n-> b(n*(16*n+1), 16*n, 2*n):
%p A204464 seq(a(n), n=0..10);
%t A204464 b[n_, i_, t_] /; i<t || n<t(t+1)/2 || n>t(2i-t+1)/2 = 0; b[0, _, _] = 1;
%t A204464 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 A204464 a[n_] := b[n(16n+1), 16n, 2n];
%t A204464 a /@ Range[0, 10] (* _Jean-François Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)
%Y A204464 Bisection of row n=8 of A204459.
%K A204464 nonn
%O A204464 0,2
%A A204464 _Alois P. Heinz_, Jan 18 2012