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Search: id:A122373
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| A122373 |
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Expansion of (c(q)^3+c(q^2)^3)/27 in powers of q where c(q) is a cubic AGM analog function. |
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| 1, 4, 9, 16, 24, 36, 50, 64, 81, 96, 120, 144, 170, 200, 216, 256, 288, 324, 362, 384, 450, 480, 528, 576, 601, 680, 729, 800, 840, 864, 962, 1024, 1080, 1152, 1200, 1296, 1370, 1448, 1530, 1536, 1680, 1800, 1850, 1920, 1944, 2112, 2208, 2304, 2451, 2404
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Expansion of eta(q^2)^5*eta(q^3)^4*eta(q^6)/eta(q)^4 in powers of q.
a(n) is multiplicative with a(2^e) = 4^e, a(3^e) = 9^e, a(p^e) = (p^(2e+2)-f^(e+1))/(p^2-f) where f = 1 if p == 1 (mod 6), f = -1 if p == 5 (mod 6).
Euler transform of period 6 sequence [ 4, -1, 0, -1, 4, -6, ...].
G.f.: Sum_{k>0} k^2*x^k/(1+x^k+x^(2k))(1+(1+(-1)^k)/8).
G.f.: Product_{k>0} (1-x^k)(1+x^(3k))(1+x^k)^5(1-x^(3k))^5.
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PROGRAM
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(PARI) {a(n)= local(A, p, e, f); if(n<0, 0, A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p<5, p^(2*e), f=-(-1)^(p%3); (p^(2*e+2)-f^(e+1))/(p^2-f)))))}
(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x^2+A)^5*eta(x^3+A)^4*eta(x^6+A)/eta(x+A)^4, n))}
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CROSSREFS
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Sequence in context: A052117 A033611 A033615 this_sequence A070458 A070457 A070456
Adjacent sequences: A122370 A122371 A122372 this_sequence A122374 A122375 A122376
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KEYWORD
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nonn,mult
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AUTHOR
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Michael Somos, Aug 30 2006
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