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A129303
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Expansion of eta(q^2)^3* eta(q^5)^2 *eta(q^10)/ eta(q)^2 in powers of q.
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3
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1, 2, 2, 4, 5, 4, 6, 8, 7, 10, 12, 8, 12, 12, 10, 16, 16, 14, 20, 20, 12, 24, 22, 16, 25, 24, 20, 24, 30, 20, 32, 32, 24, 32, 30, 28, 36, 40, 24, 40, 42, 24, 42, 48, 35, 44, 46, 32, 43, 50, 32, 48, 52, 40, 60, 48, 40, 60, 60, 40, 62, 64, 42, 64, 60, 48, 66, 64, 44, 60, 72, 56
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| Euler transform of period 10 sequence [ 2, -1, 2, -1, 0, -1, 2, -1, 2, -4, ...].
a(n) is multiplicative with a(p^e) = p^e if p = 2 or 5, a(p^e) = (p^(e+1) -1)/(p-1) if p == 1, 9 (mod 10), a(p^e) = (p^(e+1) +(-1)^e)/(p+1) if p == 3, 7 (mod 10) .
G.f.: Sum_{k>0} kronecker(20, k)* x^k/ (1-x^k)^2 .
G.f.: x* Product_{k>0} (1-x^k)* (1+x^(5*k))* (1+x^k)^3* (1-x^(5*k))^3 .
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EXAMPLE
| q + 2*q^2 + 2*q^3 + 4*q^4 + 5*q^5 + 4*q^6 + 6*q^7 + 8*q^8 + 7*q^9 + ...
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PROG
| (PARI) {a(n)= if(n<1, 0, sumdiv(n, d, n/d*kronecker(20, 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(20, 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)^3* eta(x^5 +A)^2* eta(x^10 +A)/ eta(x +A)^2, n))}
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CROSSREFS
| Sequence in context: A179821 A199088 * A138557 A186101 A202876 A128900
Adjacent sequences: A129300 A129301 A129302 * A129304 A129305 A129306
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KEYWORD
| nonn,mult
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AUTHOR
| Michael Somos, Apr 08 2007
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