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Search: id:A092877
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| A092877 |
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Expansion of (eta(q^4)/eta(q))^8 in powers of q. |
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+0
4
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| 1, 8, 44, 192, 718, 2400, 7352, 20992, 56549, 145008, 356388, 844032, 1934534, 4306368, 9337704, 19771392, 40965362, 83207976, 165944732, 325393024, 628092832, 1194744096, 2241688744, 4152367104, 7599231223, 13749863984
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Euler transform of period 4 sequence [8,8,8,0,...].
G.f. A(x) satisfies 0=f(A(x),A(x^2)) where f(u,v)=u^2-v-16uv-16v^2-256uv^2.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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G.f.: x(Product_{k>0} (1+x^(2k))/(1-x^(2k-1)))^8.
G.f.: theta_2^4/(16*theta_4^4) = lambda/(16*(1-lambda)).
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(x*prod(k=1, (n+1)\2, (1+x^(2*k))/(1-x^(2*k-1)), 1+x*O(x^n))^8, n))
(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff((eta(x^4+A)/eta(x+A))^8, n))}
(PARI) a(n)= { local(A); n--; A=x*O(x^n); polcoeff((eta(x^4 + A)/eta(x + A))^8, n); } { for(n=1, 1000, write("b092877.txt", n, " ", a(n)); ); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 21 2009]
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CROSSREFS
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Cf. A005798(n)=(-1)n*a(n).
Sequence in context: A165618 A059596 A005798 this_sequence A023007 A073380 A022636
Adjacent sequences: A092874 A092875 A092876 this_sequence A092878 A092879 A092880
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 19 2004
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