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%I #7 Aug 02 2015 21:18:20
%S 45,812,5130,20460,62335,158760,355572,722760,1361745,2413620,4068350,
%T 6574932,10252515,15502480,22821480,32815440,46214517,63889020,
%U 86866290,116348540,153731655,200624952,258871900,330571800,418102425,524143620
%N a(n) = 3rd elementary symmetric function of the first n+2 positive integers congruent to 1 mod 4.
%F From _R. J. Mathar_, Sep 15 2009: (Start)
%F a(n) = n*(2*n+3)*(n+2)*(n+1)*(4*n^2+8*n-3)/6.
%F G.f.: (27*x^3+391*x^2+497*x+45)*x/(1-x)^7. (End)
%p S := proc(n,L) mul(x+i,i=L) ; expand(%) ; coeftayl(%,x=0,nops(L)-n) ; end: A024379 := proc(n) S(3,[seq(4*j+1,j=0..n+1)]) ; end: seq(A024379(n),n=1..40) ; # _R. J. Mathar_, Sep 15 2009
%K nonn
%O 1,1
%A _Clark Kimberling_