Search: id:A006922
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%I A006922 M5160
%S A006922 1,24,324,3200,25650,176256,1073720,5930496,30178575,143184000,
%T A006922 639249300,2705114880,10914317934,42189811200,156883829400,
%U A006922 563116739584,1956790259235,6599620022400,21651325216200
%N A006922 Expansion of 1/eta(q)^24; Fourier coefficients of T_{14}.
%C A006922 Euler transform of period 1 sequence [24,24,...].
%C A006922 Equals A023021 convolved with A000041 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Jun 09 2009]
%C A006922 Equals convolution square of A005758: (1, 12, 90, 520, 2535, 10908,...) 
               [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009]
%D A006922 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006922 C. J. Moreno and A. Rocha-Caridi, The exact formula for the weight multiplicities 
               of affine Lie algebras, I, pp. 111-152 of G. E. Andrews et al., editors, 
               Ramanujan Revisited. Academic Press, NY, 1988.
%D A006922 C. L. Siegel, Advanced Analytic Number Theory, Tata Institute of Fundamental 
               Research, Bombay, 1980, pp. 249-268.
%H A006922 T. D. Noe, <a href="b006922.txt">Table of n, a(n) for n=-1..200</a>
%H A006922 R. E. Borcherds, <a href="http://www.math.berkeley.edu/~reb/papers/">
               Automorphic forms on O_{s+2,2}(R)^{+} and generalized Kac-Moody algebras</
               a>, pp. 744-752 of Proc. Intern. Congr. Math., Vol. 2, 1994.
%H A006922 <a href="Sindx_Pro.html#1mxtok">Index entries for expansions of Product_{k 
               >= 1} (1-x^k)^m</a>
%F A006922 G.f.: (1/x)(Product_{k>0} (1-x^k))^-24 = 1/\Delta (the discriminant in 
               Siegel's notation.)
%e A006922 T_{14} = 1/q + 24 + 324q + 3200q^2 + 25650q^3 + ....
%p A006922 with (numtheory): b:= proc(n) option remember; `if`(n=0, 1, add (add 
               (d*24, d=divisors(j)) *b(n-j), j=1..n)/n) end: a:= n->b(n+1): seq 
               (a(n), n=-1..40); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Oct 17 2008]
%o A006922 (PARI) a(n)=if(n<-1,0,n++; polcoeff(eta(x+x*O(x^n))^-24,n))
%Y A006922 Cf. A000594, A048057, A048100, A048101, A048110, A048145.
%Y A006922 Cf. 24th column of A144064. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Oct 17 2008]
%Y A006922 A023021, A000041 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 09 
               2009]
%Y A006922 A005758 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009]
%Y A006922 Sequence in context: A053215 A004413 A069779 this_sequence A036221 A022652 
               A138453
%Y A006922 Adjacent sequences: A006919 A006920 A006921 this_sequence A006923 A006924 
               A006925
%K A006922 nonn,easy,nice
%O A006922 -1,2
%A A006922 N. J. A. Sloane (njas(AT)research.att.com).
%E A006922 More terms from Barry Brent (barryb(AT)primenet.com)

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