OFFSET
1,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
Michael Somos, A Remarkable eta-product Identity
FORMULA
G.f.: x Product_{k>0} (1-x^(3k))(1-x^(5k))(1-x^(6k))(1-x^(10k)) + x^2 Product_{k>0} (1-x^k)(1-x^(2k))(1-x^(15k))(1-x^(30k)).
a(n) = -A030184(2*n).
PROG
(PARI) {a(n) = my(A); if( n<1, 0, n*=2; n--; A = x * O(x^n); polcoeff( -eta(x + A) * eta(x^3 + A) * eta(x^5 + A) * eta(x^15 + A), n))};
(PARI) {a(n) = my(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^3 + A) * eta(x^5 + A) * eta(x^6 + A) * eta(x^10 + A) + eta(x+A) * eta(x^2 + A) * eta(x^15 + A) * eta(x^30 + A)*x, n))};
(PARI) {a(n) = my(A, p, e, x, y, a0, a1); if( n<1, 0, A = factor(n); prod(k=1, matsize(A)[1], [p, e] = A[k, ]; if(p==3, (-1)^e, p==5, 1, a0=1; y=if(p==2, a1=1; -1, a1=-sum(x=0, p-1, kronecker(4*x^3+5*x^2+2*x+1, p))); for(i=2, e, x=y*a1-p*a0; a0=a1; a1=x); a1)))};
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Michael Somos, Sep 10 2006
STATUS
approved