Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I M3190 #20 Nov 25 2015 12:18:28
%S 1,0,4,0,14,8,40,32,105,112,284,320,702,840,1688,2112,3860,4976,8540,
%T 11264,18424,24480,38584,51520,78901,105648,157600,211136,308310,
%U 412872,592224,791040,1117441,1488160,2074924,2754048,3794660,5018408
%N Expansion of eta(q^10)^12/(eta(q^2)^4*eta(q^5)^8) in powers of q.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Morris Newman, <a href="http://plms.oxfordjournals.org/content/s3-9/3/373.extract">Construction and application of a class of modular functions (II)</a>. Proc. London Math. Soc. (3) 9 1959 373-387. MR0107629 (21 #6354)
%H Morris Newman, <a href="/A002507/a002507.pdf">Construction and application of a class of modular functions, II</a>, Proc. London Math. Soc. (3) 9 1959 373-387. [Annotated scanned copy, barely legible]
%F Euler transform of period 10 sequence [0, 4, 0, 4, 8, 4, 0, 4, 0, 0, ...]. - _Michael Somos_, Nov 10 2005
%e q^3 + 4*q^5 + 14*q^7 + 8*q^8 + 40*q^9 + 32*q^10 + 105*q^11 + 112*q^12 + ...
%t 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 *)
%o (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 */
%K nonn,easy
%O 3,3
%A _N. J. A. Sloane_