A279613 Expansion of the g.f. of A160534 in powers of A121593.

1, -7, 42, -231, 1155, -4998, 15827, -791, -566244, 6506955, -53524611, 369879930, -2218053747, 11306008875, -43772711220, 55203364377, 1172838094533, -16542312772356, 150992704165079, -1130142960861845, 7290759457923816

Offset: 1

Author

Lynette O'Brien, Dec 15 2016

Keywords

• sign

Comments

(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.

Examples

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

References

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

Links

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

Crossrefs

Cf. A183204, A229111, A279618, A279619.

Formula

(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...