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1, -7, 42, -231, 1155, -4998, 15827, -791, -566244, 6506955, -53524611, 369879930, -2218053747, 11306008875, -43772711220, 55203364377, 1172838094533, -16542312772356, 150992704165079, -1130142960861845, 7290759457923816
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OFFSET
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1,2
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COMMENTS
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(eta(q))^7/eta(7*q) in powers of (eta(7*q)/eta(q))^4.
This sequence is u_n in Theorem 6.5 in O'Brien's thesis.
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REFERENCES
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L. O'Brien, Modular forms and two new integer sequences at level 7, Massey University, 2016.
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LINKS
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FORMULA
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(n+1)^4a_7(n+1)=-(26*n^4+52*n^3+58*n^2+32*n+7)a_7(n)-(267*n^4+268*n^2+18)a_7(n-1)-(1274*n^4-2548*n^3+2842*n^2-1568*n+343)a_7(n-2)-2401(n-1)^4a_7(n-3)
with a_7(0)=1, a_7(-1)=a_7(-2)=a_7(-3)=0.
asymptotic conjecture: a(n) ~ C n^(-4/3) 7^n cos( n( arctan( (3*sqrt 3)/13) +Pi -1.083913253)), where C = 6.502807770...
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EXAMPLE
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G.f.: 1 - 7*x + 42*x^2 - 231*x^3 + 1155*x^4 - 4998*x^5 + ...
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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