|
Search: id:A132975
|
|
|
| A132975 |
|
Expansion of q * psi(-q^9) / psi(-q) in powers of q where psi() is a Ramanujan theta function. |
|
+0
5
|
|
| 1, 1, 1, 2, 3, 4, 5, 7, 10, 12, 15, 20, 26, 32, 39, 50, 63, 76, 92, 114, 140, 168, 201, 244, 295, 350, 415, 496, 591, 696, 818, 967, 1140, 1332, 1554, 1820, 2126, 2468, 2861, 3324, 3855, 4448, 5126, 5916, 6816, 7824, 8970, 10292, 11793, 13471, 15372, 17548
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
FORMULA
|
Expansion of eta(q^2) * eta(q^9) * eta(q^36) / (eta(q) * eta(q^4) * eta(q^18)) in powers of q.
Euler transform of period 36 sequence [ 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6) = u1 * u2 - (1 + u1 + u2) * (u3 + u6 + 3 * u3 * u6).
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = (1/3) / f(t) where q = exp(2 pi i t).
G.f.: x * Product_{k>0} P(3,x^k) * P(9,x^k) * P(12,x^k) * P(36,x^k) where P(n,x) is the n-th cyclotomic polynomial.
|
|
EXAMPLE
|
q + q^2 + q^3 + 2*q^4 + 3*q^5 + 4*q^6 + 5*q^7 + 7*q^8 + 10*q^9 + ...
|
|
PROGRAM
|
(PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^9 + A) * eta(x^36 + A) / ( eta(x + A) * eta(x^4 + A) * eta(x^18 + A) ), n))}
|
|
CROSSREFS
|
Convolution inverse of A132976.
A132972(n) = 3 * a(n) unless n=0. A128129(n) = a(2*n). A132302(n) = a(2*n+1). A128640(n) = a(3*n).
Sequence in context: A036028 A036033 A124243 this_sequence A145977 A050729 A117536
Adjacent sequences: A132972 A132973 A132974 this_sequence A132976 A132977 A132978
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Michael Somos, Sep 07 2007
|
|
|
Search completed in 0.002 seconds
|
