This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A279618 #28 Sep 07 2018 12:30:41
%S A279618 1,-9,30,-15,-240,978,-1463,-2361,18201,-42800,15624,227742,-809028,
%T A279618 1088367,1593120,-11383551,25003158,-8589729,-119069358,403991280,
%U A279618 -521730930,-736063496,5088063696,-10843708302,3624181875,48991048836,-162420646812,205328313785,284014016994
%N A279618 Expansion of w_7/(1 + 13*w_7 + 49*w_7^2) in powers of q, where w_7 = (eta(7*q)/eta(q))^4.
%C A279618 G.f. is y_7 in Cooper's paper.
%C A279618 See Equation (3.15) and Theorem 3.10 in O'Brien's thesis.
%C A279618 G.f. is a period 1 Fourier series which satisfies f(-1 / (7 t)) = f(t) where q = exp(2 Pi i t). - _Michael Somos_, Sep 07 2018
%D A279618 S. Cooper, (2012). Sporadic sequences, modular forms and new series for 1/pi. The Ramanujan Journal, 29(1-3), 163-183.
%D A279618 L. O'Brien, Modular forms and two new integer sequences at level 7, Massey University, 2016.
%H A279618 Lynette O'Brien, <a href="https://www.researchgate.net/profile/Lynette_Obrien">Modular forms and two new integer sequences at level 7</a>
%H A279618 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 A279618 G.f. is w_7/(1 + 13*w_7 + 49*w_7^2) = (eta(q)*eta(7q)/z_7)^3 where w_7 = (eta(7*q)/eta(q))^4 and z_7 = 1 + 2*Sum_{k>0} Kronecker(-7,k)*q^k/(1-q^k).
%F A279618 G.f. is also (eta(q)*eta(7*q)/z_7)^3, where z_7 = 1 + 2*Sum_{k>0} Kronecker(-7,k)*q^k/(1-q^k). See A002652.
%e A279618 G.f. = q - 9*q^2 + 30*q^3 - 15*q^4 - 240*q^5 + 978*q^6 - 1463*q^7 + ...
%t A279618 a[ n_] := With[{u1 = QPochhammer[ x]^4, u7 = QPochhammer[ x^7]^4}, SeriesCoefficient[ x u1 u7 / (u1^2 + 13 x u1 u7 + 49 x^2 u7^2) , {x, 0, n}]]; (* _Michael Somos_, Sep 07 2018 *)
%o A279618 (PARI) {a(n) = my(A); if( n<1, 0, A = x * O(x^n); A = x * (eta(x^7 + A) / eta(x + A))^4; polcoeff( 1 / (1/A + 13 + 49*A), n))}; /* _Michael Somos_, Sep 07 2018 */
%Y A279618 Cf. A002652, A121593, A279613, A279619.
%K A279618 sign
%O A279618 1,2
%A A279618 _Lynette O'Brien_, Dec 15 2016