A225699 Numerators of coefficients arising from q-expansion of Integrate[eta[q^4]^8/eta[q^2]^4, q]/q where eta is the Dedekind eta function.

1, 1, 1, 1, 13, 1, 1, 3, 1, 1, 16, 1, 31, 10, 1, 1, 24, 4, 1, 7, 1, 1, 39, 1, 57, 18, 1, 9, 40, 1, 1, 13, 14, 1, 48, 1, 1, 31, 16, 1, 121, 1, 54, 15, 1, 28, 64, 5, 1, 39, 1, 1, 96

Offset

0,5

Comments

Gosper observes that A225699/A225700 = A008438/(2,4,6,8,10,...) and hence the coefficient of q^k in the q-expansion is 1 iff k is an odd prime (see Example section below).

Note that, as usual in the OEIS, the q-expansion has been normalized here to avoid having every other term be zero.

References

R. W. Gosper, Posting to the Math Fun Mailing List, Jun 01 2013

Links

Table of n, a(n) for n=0..52.

Example

q/2 + q^3 + q^5 + q^7 + (13*q^9)/10 + q^11 + q^13 + (3*q^15)/2 + q^17 + q^19 + (16*q^21)/11 + q^23 + (31*q^25)/26 + (10*q^27)/7 + q^29 + q^31 + (24*q^33)/17 + (4*q^35)/3 + q^37 + (7*q^39)/5 + q^41 + q^43 + (39*q^45)/23 + q^47 + (57*q^49)/50 + (18*q^51)/13 + q^53 + (9*q^55)/7 + (40*q^57)/29 + q^59 + q^61 + (13*q^63)/8 + (14*q^65)/11 + q^67 + (48*q^69)/35 + q^71 + q^73 + (31*q^75)/19 + (16*q^77)/13 + q^79 + (121*q^81)/82 + q^83 + (54*q^85)/43 + (15*q^87)/11 + q^89 + (28*q^91)/23 + (64*q^93)/47 + (5*q^95)/4 + q^97 + (39*q^99)/25 + q^101 + q^103 + (96*q^105)/53 + ...

Crossrefs

Cf. A225700. See A008438 for eta[q^4]^8/eta[q^2]^4.

Sequence in context: A010227 A010228 A293218 * A010226 A066834 A010225

Adjacent sequences: A225696 A225697 A225698 * A225700 A225701 A225702

Keyword

nonn,frac

Author

N. J. A. Sloane, Jun 01 2013

Status

approved