A064511 Ramanujan's function F_5(q).

1, 10, 0, 0, -30, 30, -20, 0, 0, 70, -20, 120, 0, 0, -60, 40, -110, 0, 0, 200, -90, 120, 0, 0, -100, 130, -120, 0, 0, 300, -60, 320, 0, 0, -160, 120, -210, 0, 0, 240, -100, 420, 0, 0, -360, 210, -220, 0, 0, 430, -120, 320, 0, 0, -200, 360, -300, 0, 0, 600, -120, 620

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

S. Ahlgren, The sixth, eighth, ninth and tenth powers of Ramanujan's theta function, Proc. Amer. Math. Soc., 128 (1999), 1333-1338; F_5(q).

Formula

subs(q=-q, f)^5/subs(q=-q^5, f)+5*q*subs(q=-q^5, f)^5/subs(q=-q, f), where f = A010815 = Sum_{k=-infinity, infinity} (-1)^k*q^(k*(3*k-1)/2).

Example

G.f. = 1 + 10*q - 30*q^4 + 30*q^5 - 20*q^6 + 70*q^9 - 20*q^10 + 120*q^11 - 60*q^14 + ...

Mathematica

f[q_] := Sum[(-1)^k*q^(k*(3*k - 1)/2), {k, - Infinity, Infinity}];
CoefficientList[Series[f[-q]^5/f[-q^5] + 5*q*f[-q^5]^5/f[-q], {q, 0, 70}], q] (* G. C. Greubel, May 29 2019 *)

Crossrefs

See A000122 for F_2, A004016 for F_3, A004013 for F_4, A064511 (this sequence) for F_5, A064512 for F_7.

Sequence in context: A167165 A288435 A287734 * A341809 A340947 A306934

Adjacent sequences: A064508 A064509 A064510 * A064512 A064513 A064514

Keyword

sign

Author

N. J. A. Sloane, Oct 06 2001

Status

approved