Search: id:A035315
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%I A035315
%S A035315 1,264,8244,139520,1672290,15872256,126745880,884100096,5525046495,
%T A035315 31498809600,166049246340,817866616320,3794952949854,16699329285120,
%U A035315 70071039813240,281650911606784,1088671630120515,4060062852952320
%N A035315 Fourier coefficients of T_{10}.
%C A035315 T_{10} is the unique weight = -8 normalized meromorphic modular form 
               for SL(2,Z) with all poles at infinity.
%D A035315 C. L. Siegel, Advanced Analytic Number Theory,Tata Institute of Fundamental 
               Research, Bombay, 1980, pp. 249-268.
%H A035315 Borcherds, Richard E., <a href="http://arXiv.org/abs/alg-geom/9609022">
               Automorphic forms with singularities on Grassmannians</a>, Invent. 
               Math. 132 (1998), 491-562.
%F A035315 G.f. = G_4/Delta (in Siegel's notation.)
%e A035315 T_{10} = 1/q + 264 + 8244 q + ....
%o A035315 (PARI) {a(n)=if(n<-1, 0, n++; polcoeff( sum(k=1,n,240*sigma(k,3)*x^k,
               1+x*O(x^n))/eta(x+x*O(x^n))^24,n))} /* Michael Somos Apr 12 2005 
               */
%Y A035315 Sequence in context: A092724 A112069 A022043 this_sequence A107507 A013974 
               A145639
%Y A035315 Adjacent sequences: A035312 A035313 A035314 this_sequence A035316 A035317 
               A035318
%K A035315 easy,nonn
%O A035315 -1,2
%A A035315 Barry Brent (barryb(AT)primenet.com)

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