A024379 a(n) = 3rd elementary symmetric function of the first n+2 positive integers congruent to 1 mod 4.

45, 812, 5130, 20460, 62335, 158760, 355572, 722760, 1361745, 2413620, 4068350, 6574932, 10252515, 15502480, 22821480, 32815440, 46214517, 63889020, 86866290, 116348540, 153731655, 200624952, 258871900, 330571800, 418102425, 524143620

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Programs

Maple

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

Formula

From R. J. Mathar, Sep 15 2009: (Start)

a(n) = n*(2*n+3)*(n+2)*(n+1)*(4*n^2+8*n-3)/6.

G.f.: (27*x^3+391*x^2+497*x+45)*x/(1-x)^7. (End)