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%I #19 Dec 17 2021 09:24:35
%S 1,1,4,6,15,24,49,78,141,219,364,550,861,1261,1884,2682,3856,5350,
%T 7452,10100,13699,18183,24104,31404,40816,52297,66809,84334,106110,
%U 132164,164062,201896,247626,301429,365727,440818,529656,632693
%N Molien series for Hecke group H_{3,4}.
%H Bernhard Runge, <a href="http://projecteuclid.org/euclid.nmj/1118775400">On Siegel modular forms, part II</a>, Nagoya Math. J. 138, 179-197 (1995)
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_26">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -3, 0, -1, 3, 1, -4, 2, 0, 2, 1, -6, 1, 2, 0, 2, -4, 1, 3, -1, 0, -3, 1, 2, -1).
%F G.f.: N_Hecke(x)*(1 + x^2)/((1 - x^2)*(1 - x^4)^3*(1 - x^6)*(1 - x^8)*(1 - x^12)*(1 - x^14)) where N_Hecke(x)= 1 - x^2 + x^4 + 2*x^8 + x^10 + 2*x^12 + x^14 + 5*x^16 + x^18 + 6*x^20 + 2*x^22 + 6*x^24 + 2*x^26 + 6*x^28 + x^30 + 5*x^32 + x^34 + 2*x^36 + x^38 + 2*x^40 + x^44 - x^46 + x^48.
%t ker = {2, 1, -3, 0, -1, 3, 1, -4, 2, 0, 2, 1}; LinearRecurrence[Join[ker, {-6}, Reverse[ker], {-1}], {1, 1, 4, 6, 15, 24, 49, 78, 141, 219, 364, 550, 861, 1261, 1884, 2682, 3856, 5350, 7452, 10100, 13699, 18183, 24104, 31404, 40816, 52297}, 40] (* _Jean-François Alcover_, Jun 11 2017 *)
%K nonn,easy,nice
%O 0,3
%A _N. J. A. Sloane_
%E More terms and formula from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 24 2001
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