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A124815
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Expansion of (eta(q^2)*eta(q^3)/eta(q))^2*eta(q^4)*eta(q^12) in powers of q.
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0
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1, 2, 3, 4, 4, 6, 6, 8, 9, 8, 12, 12, 14, 12, 12, 16, 16, 18, 18, 16, 18, 24, 24, 24, 21, 28, 27, 24, 28, 24, 30, 32, 36, 32, 24, 36, 38, 36, 42, 32, 40, 36, 42, 48, 36, 48, 48, 48, 43, 42, 48, 56, 52, 54, 48, 48, 54, 56, 60, 48, 62, 60, 54, 64, 56, 72, 66, 64, 72, 48, 72, 72
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| Euler transform of period 12 sequence [ 2, 0, 0, -1, 2, -2, 2, -1, 0, 0, 2, -4, ...].
Multiplicative with a(p^e) = p^e if p<5, a(p^e) = (p^(e+1)-1)/(p-1) if p == 1, 11 (mod 12), a(p^e) = (p^(e+1)+(-1)^e)/(p+1) if p == 5, 7 (mod 12).
G.f.: Sum_{k>0} k*x^k*(1-x^(2k))/(1-x^(2k)+x^(4k)) = x*Product_{k>0} (1+x^k)^2*(1-x^(3k))^2*(1-x^(4k))*(1-x^(12k)).
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PROG
| (PARI) {a(n)=if(n<1, 0, sumdiv(n, d, n/d*kronecker(12, d)))}
(PARI) {a(n)=local(A, p, e, f); if(n<1, 0, A=factor(n); prod( k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; f=kronecker(12, p); (p^(e+1)-f^(e+1))/(p-f))))}
(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x^2+A)^2*eta(x^3+A)^2* eta(x^4+A)*eta(x^12+A)/eta(x+A)^2, n))}
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CROSSREFS
| Sequence in context: A102443 A102441 A102440 * A081328 A179276 A205787
Adjacent sequences: A124812 A124813 A124814 * A124816 A124817 A124818
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KEYWORD
| nonn,mult
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AUTHOR
| Michael Somos, Nov 08 2006
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