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%I #14 May 10 2014 09:51:48
%S 1,1,7,9,56,79,470,697,4048,6196,35443,55455,313912,499178,2804012,
%T 4514873,25211936,40999516,227881004,373585604,2068564064,3414035527,
%U 18844224462,31278197839,172186125456,287191809724,1577401391626,2642070371194,14483100716176,24347999094724
%N Numbers of vectors with 2*n integers such that each element is either 1 or -1, and their sum > n.
%F a(n) = sum_{k = 1+floor(n/2)...n} binomial(2n,n-k), sum of the n/2 rightmost elements of row n of A094527. - _Giovanni Resta_, May 31 2013
%e With n=3 there are 7 vectors with sum bigger than 3:
%e {1, 1, 1, 1, 1, 1}
%e {-1, 1, 1, 1, 1, 1}
%e {1, -1, 1, 1, 1, 1}
%e {1, 1, -1, 1, 1, 1}
%e {1, 1, 1, -1, 1, 1}
%e {1, 1, 1, 1, -1, 1}
%e {1, 1, 1, 1, 1, -1}
%e So a(3) = 7.
%p A226197 := proc(n)
%p add( A094527(n,k),k=1+floor(n/2)..n) ;
%p end proc: # _R. J. Mathar_, Jun 04 2013
%t a[n_] := Sum[(2*n)!/((n-k)!*(n+k)!), {k, 1 + Floor[n/2], n}]; Array[a,30] (* _Giovanni Resta_, May 31 2013 *)
%o (C)
%o #include <stdio.h>
%o long long count, n;
%o void addOne(long long sum, long long added) {
%o if (added==n*2) {
%o if (sum>n) ++count;
%o return;
%o }
%o ++added;
%o addOne(sum+1, added);
%o addOne(sum-1, added);
%o }
%o int main() {
%o for (n=1; n<99; n++) {
%o count = 0;
%o addOne(0, 0);
%o printf("%llu, ", count);
%o }
%o return 0;
%o }
%K nonn
%O 1,3
%A _Alex Ratushnyak_, May 31 2013
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