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Expansion of the g.f. of A160534 in powers of A121593.
2

%I #15 Dec 24 2016 09:26:16

%S 1,-7,42,-231,1155,-4998,15827,-791,-566244,6506955,-53524611,

%T 369879930,-2218053747,11306008875,-43772711220,55203364377,

%U 1172838094533,-16542312772356,150992704165079,-1130142960861845,7290759457923816

%N Expansion of the g.f. of A160534 in powers of A121593.

%C (eta(q))^7/eta(7*q) in powers of (eta(7*q)/eta(q))^4.

%C This sequence is u_n in Theorem 6.5 in O'Brien's thesis.

%D L. O'Brien, Modular forms and two new integer sequences at level 7, Massey University, 2016.

%H L. O'Brien, <a href="https://doi.org/10.13140/RG.2.2.33912.03843">Modular forms and two new integer sequences at level 7</a>, Massey University, 2016.

%F (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)

%F with a_7(0)=1, a_7(-1)=a_7(-2)=a_7(-3)=0.

%F asymptotic conjecture: a(n) ~ C n^(-4/3) 7^n cos( n( arctan( (3*sqrt 3)/13) +Pi -1.083913253)), where C = 6.502807770...

%e G.f.: 1 - 7*x + 42*x^2 - 231*x^3 + 1155*x^4 - 4998*x^5 + ...

%Y Cf. A183204, A229111, A279618, A279619.

%K sign

%O 1,2

%A _Lynette O'Brien_, Dec 15 2016