|
Search: id:A129303
|
|
|
| A129303 |
|
Expansion of eta(q^2)^3* eta(q^5)^2 *eta(q^10)/ eta(q)^2 in powers of q. |
|
+0
4
|
|
| 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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
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 .
|
|
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 + ...
|
|
PROGRAM
|
(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))}
|
|
CROSSREFS
|
Sequence in context: A137605 A133082 A130265 this_sequence A138557 A128900 A136099
Adjacent sequences: A129300 A129301 A129302 this_sequence A129304 A129305 A129306
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
Michael Somos, Apr 08 2007
|
|
|
Search completed in 0.002 seconds
|
