A006710 Expansion of eta(q^10)^12/(eta(q^2)^4*eta(q^5)^8) in powers of q. (Formerly M3190)

1, 0, 4, 0, 14, 8, 40, 32, 105, 112, 284, 320, 702, 840, 1688, 2112, 3860, 4976, 8540, 11264, 18424, 24480, 38584, 51520, 78901, 105648, 157600, 211136, 308310, 412872, 592224, 791040, 1117441, 1488160, 2074924, 2754048, 3794660, 5018408

Offset

3,3

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=3..40.

Morris Newman, Construction and application of a class of modular functions (II). Proc. London Math. Soc. (3) 9 1959 373-387. MR0107629 (21 #6354)

Morris Newman, Construction and application of a class of modular functions, II, Proc. London Math. Soc. (3) 9 1959 373-387. [Annotated scanned copy, barely legible]

Formula

Euler transform of period 10 sequence [0, 4, 0, 4, 8, 4, 0, 4, 0, 0, ...]. - Michael Somos, Nov 10 2005

Example

q^3 + 4*q^5 + 14*q^7 + 8*q^8 + 40*q^9 + 32*q^10 + 105*q^11 + 112*q^12 + ...

Mathematica

QP = QPochhammer; s = QP[q^10]^12/(QP[q^2]^4*QP[q^5]^8) + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 25 2015 *)

Prog

(PARI) {a(n)=local(A); if(n<3, 0, n-=3; A=x*O(x^n); polcoeff( eta(x^10+A)^12/eta(x^2+A)^4/eta(x^5+A)^8, n))} /* Michael Somos, Nov 10 2005 */

Crossrefs

Sequence in context: A117786 A117788 A233398 * A141150 A081162 A095367

Adjacent sequences: A006707 A006708 A006709 * A006711 A006712 A006713

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved