0,13

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

B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 258 Entry 9(iii).

Euler transform of period 20 sequence [1, -1, 1, 0, 0, -1, 1, 0, 1, -2, 1, 0, 1, -1, 0, 0, 1, -1, 1, -2, ...]. - Michael Somos, Apr 25 2003

G.f.: product((1-q^(10*i))^2*(1-q^(10*i-5))*(1-q^(4*i-2))/((1-q^(2*i-1))*(1-q^(20*i-10))), i=1..200)

G.f.: Product_{n>0} (1-x^(10n))^2(1+x^(2n-1))/(1+x^(10n-5)). - Michael Somos, Apr 25 2003

a(n)=b(n+1) where b(n) is multiplicative and b(2^e) = b(5^e) = 1, b(p^e) = e+1 if p == 1, 5 (mod 8), b(p^e) = (1+(-1)^e)/2 if p == 3, 7 (mod 8).

G.f.: (phi(x)^2-phi(x^5)^2)/(4x) = chi(x)f(-x^5)f(-x^20) where phi(), chi(), f() are Ramanujan theta functions

Expansion of q^(-1)eta(q^2)^2eta(q^5)eta(q^20)/(eta(q)eta(q^4)) in powers of q. - Michael Somos, Apr 25 2003

(PARI) a(n)=if(n<0, 0, polcoeff(prod(k=0, n\2, 1+x^(2*k+1), 1+x*O(x^n))*prod(k=0, n\10, (1-x^(10*k+10))^2/(1+x^(10*k+5)), 1+x*O(x^n)), n))

(PARI) a(n)=if(n<0, 0, n++; sumdiv(n, d, kronecker(-100, d)))

(PARI) a(n)=if(n<0, 0, n++; direuler(p=2, n, 1/(1-X)/(1-kronecker(-100, p)*X))[n])

(PARI) a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff(eta(x^2+A)^2*eta(x^5+A)*eta(x^20+A)/eta(x+A)/eta(x^4+A), n))

A122190(n)=a(4n).

Sequence in context: A001899 A059882 A094247 this_sequence A085862 A024942 A049321

Adjacent sequences: A053691 A053692 A053693 this_sequence A053695 A053696 A053697

easy,nice,nonn

James A. Sellers (sellersj(AT)math.psu.edu), Feb 14 2000