0,3

B. C. Berndt, H. H. Chan, S.-S. Huang, S.-Y. Kang, J. Sohn and S. H. Son, The Rogers-Ramanujan continued fraction, J. Comput. Appl. Math. 105 (1999), 9-24.

Garvan, F., Kim, D. and Stanton, D., Cranks and t-cores, Inventiones Math. 101 (1990), 1-17.

Freeman J. Dyson, Missed opportunities, Bull. Amer. Math. Soc. 78 (1972), 635-652. see pages 636-637.

T. D. Noe, Table of n, a(n) for n=0..1000

B. C. Berndt, The Rogers-Ramanujan continued fraction.

F. Garvan, D. Kim and D. Stanton, Cranks and t-cores.

Given g.f. A(x), then B(x)=x*A(x) satisfies 0=f(B(x), B(x^2), B(x^4)) where f(u, v, w)=v^3+2uvw+4uw^2-u^2w. - Michael Somos May 02 2005

G.f.: (1/x)(Sum_{k>0} kronecker(k, 5)*x^k/(1-x^k)^2) . - Michael Somos Sep 02 2005

G.f.: Product_{k>0} (1-x^(5k))^5/(1-x^k) = 1/x(Sum_{k>0} k*x^k(1-x^k)(1-x^(2k))/(1-x^(5k))) . - Michael Somos Jun 17 2005

Euler transform of period 5 sequence [ 1, 1, 1, 1, -4, ...].

Expansion of q^(-1)* eta(q^5)^5/ eta(q) in powers of q.

a(n)=b(n+1) where b(n) is multiplicative with b(5^e) = 5^e, b(p^e) = (p^(e+1)-1)/ (p-1) if p == 1, 4 (mod 5), b(p^e) = (p^(e+1)+(-1)^e)/ (p+1) if p == 2, 3 (mod 5).

G.f.: x^(-1)* Sum_{a,b,c,d,e} x^((a^2 +b^2 +c^2 +d^2 +e^2)/ 10) where a+b+c+d+e=0, (a,b,c,d,e) == (0,1,2,3,4) (mod 5). - Michael Somos Aug 08 2007

(PARI) a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff(eta(x^5+A)^5/eta(x+A), n))

(PARI) a(n)=if(n<0, 0, n++; sumdiv(n, d, kronecker(d, 5)*n/d))

(PARI) a(n)=if(n<0, 0, n++; direuler(p=2, n, 1/(1-p*X)/(1-kronecker(p, 5)*X))[n])

Cf. A053724.

Sequence in context: A125766 A093870 A126833 this_sequence A138512 A066949 A073481

Adjacent sequences: A053720 A053721 A053722 this_sequence A053724 A053725 A053726

easy,nonn,mult

James A. Sellers (sellersj(AT)math.psu.edu), Feb 11 2000