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A006710 Expansion of eta(q^10)^12/(eta(q^2)^4*eta(q^5)^8) in powers of q.
(Formerly M3190)
0
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified November 24 10:26 EST 2020. Contains 338612 sequences. (Running on oeis4.)