# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a341574 Showing 1-1 of 1 %I A341574 #10 Aug 01 2023 08:08:17 %S A341574 0,1,3,-855,-19719,-189663,-809226,-255339,9868542,24108075,-19076611, %T A341574 -83250516,-178059060,-774131094,1654990113,4979928843,-8282963151, %U A341574 7132715646,-6849297108,-29601661516,-8702922246,87845108229,5032903977,141218051814,-264089426616,302320735992,-825532125819 %N A341574 Fourier coefficients of the modular form (1/t_{6a}^3) * (1-6*sqrt(-3)/t_{6a}) * (1-12*sqrt(-3)/t_{6a})^(4/3) * F_{6a}^20. %C A341574 Here, F_{6a} is the hypergeometric function F(1/3, 1/2; 1; 12*sqrt(-3)/t_{6a}). The definition given on page 23 in the linked manuscript has a minor typo where "t_{3A}" should be "t_{6a}". - _Robin Visser_, Jul 31 2023 %H A341574 Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021. Sloane wrote 2005 on the first page but the internal evidence suggests 1997.] See page 31. %o A341574 (Sage) %o A341574 def a(n): %o A341574 if n==0: return 0 %o A341574 theta2 = sum([1]+[2*x^(k^2/2) for k in range(1, n+1)]) %o A341574 theta3 = sum([2*x^((k^2 + k + 1/4)/2) for k in range(n)]) %o A341574 phix = theta2(x=x^4)*theta2(x=x^12) + theta3(x=x^4)*theta3(x=x^12) %o A341574 phiy = theta2(x=x^4)*theta3(x=x^12) + theta3(x=x^4)*theta2(x=x^12) %o A341574 f = (phiy^3*(phix^2-phiy^2)^3*phix*(phix^2-9*phiy^2)*(phix^2+3*phiy^2)^4)/8 %o A341574 return f.taylor(x, 0, n+1).coefficient(x^(n+1/2)) # _Robin Visser_, Jul 31 2023 %K A341574 sign %O A341574 0,3 %A A341574 _Robert C. Lyons_, Feb 15 2021 %E A341574 More terms from _Robin Visser_, Jul 31 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE