-1,2

Euler transform of period 1 sequence [24,24,...].

Equals A023021 convolved with A000041 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 09 2009]

Equals convolution square of A005758: (1, 12, 90, 520, 2535, 10908,...) [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

C. L. Siegel, Advanced Analytic Number Theory, Tata Institute of Fundamental Research, Bombay, 1980, pp. 249-268.

T. D. Noe, Table of n, a(n) for n=-1..200

R. E. Borcherds, Automorphic forms on O_{s+2,2}(R)^{+} and generalized Kac-Moody algebras, pp. 744-752 of Proc. Intern. Congr. Math., Vol. 2, 1994.

Index entries for expansions of Product_{k >= 1} (1-x^k)^m

G.f.: (1/x)(Product_{k>0} (1-x^k))^-24 = 1/\Delta (the discriminant in Siegel's notation.)

T_{14} = 1/q + 24 + 324q + 3200q^2 + 25650q^3 + ....

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]

(PARI) a(n)=if(n<-1, 0, n++; polcoeff(eta(x+x*O(x^n))^-24, n))

Cf. A000594, A048057, A048100, A048101, A048110, A048145.

Cf. 24th column of A144064. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]

A023021, A000041 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 09 2009]

A005758 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009]

Sequence in context: A053215 A004413 A069779 this_sequence A036221 A022652 A138453

Adjacent sequences: A006919 A006920 A006921 this_sequence A006923 A006924 A006925

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Barry Brent (barryb(AT)primenet.com)