0,2

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

M. Boylan, Exceptional congruences for the coefficients of certain eta-product newforms, J. Number Theory 98 (2003), no. 2, 377-389.

M. Koike, On McKay's conjecture, Nagoya Math. J., 95 (1984), 85-89.

Newman, Morris; A table of the coefficients of the powers of $\eta(\tau)$. Nederl. Akad. Wetensch. Proc. Ser. A. 59 = Indag. Math. 18 (1956), 204-216.

J. H. Silverman, A Friendly Introduction to Number Theory, 3rd ed., Pearson Education, Inc, 2006, p. 415. Exer. 47.2.

Robert M. Ziff, "On Cardy's formula for the critical crossing probability in 2d percolation," J. Phys. A. 28, 1249-1255 (1995).

S. R. Finch, Powers of Euler's q-Series, (arXiv:math.NT/0701251).

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

Euler transform of period 1 sequence [ -4, -4, ...]. - Michael Somos Apr 2 2005

Given g.f. A(x), then B(x)=x*A(x^3)^2 satisfies 0=f(B(x), B(x^2), B(x^4)) where f(u, v, w)=wu^2-v^3+16uw^2. - Michael Somos Apr 2 2005

a(n)=b(6n+1) and b(n) is multiplicative with b(2^e)=b(3^e)=0^e, b(p^e)=b(p)b(p^(e-1))-p*b(p^(e-2)), b(p)=0 if p == 5 (mod 6), b(p)=2x where p=x^2+3y^2 == 1 (mod 6) and x == 1 (mod 3). - Michael Somos Aug 23 2006

Coefficients of L-series for elliptic curve "36a1": y^2= x^3 +1 . - Michael Somos Jul 1 2004

with (numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add (add (d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: a:= etr (n-> -4): seq (a(n), n=0..81); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008]

(PARI) {a(n)= local(A, p, e, x, y, a0, a1); if(n<0, 0, n=6*n+1; A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p<5, 0, if(p%6==5, if(e%2, 0, (-1)^(e/2)*p^(e/2)), for(y=1, sqrtint(p\3), if(issquare(p-3*y^2, &x), break)); a0=1; if(x%3!=1, x=-x); a1=x=2*x; for(i=2, e, y=x*a1-p*a0; a0=a1; a1=y); a1)))))} /* Michael Somos Aug 23 2006 */

(PARI) {a(n)= if(n<0, 0, polcoeff(eta(x +x*O(x^n))^4, n))}

(PARI) {a(n)= if(n<0, 0, n= 6*n +1; ellak( ellinit( [0, 0, 0, 0, 1]), n))} /* Michael Somos Jul 1 2004 */

Sequence in context: A143095 A141073 A131819 this_sequence A030181 A021879 A020806

Adjacent sequences: A000724 A000725 A000726 this_sequence A000728 A000729 A000730

sign

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