|
Search: id:A133738
|
|
|
| A133738 |
|
Expansion of product of 3rd order mock theta function phi(q) and Ramanujan theta function f(-q). |
|
+0
1
|
|
| 1, 0, -2, -2, 2, 2, -2, 0, 2, 4, -2, -4, 2, 0, -2, -2, 2, 4, -4, -4, 2, 2, -2, 0, 4, 4, 0, -6, 2, 0, -2, 0, 2, 6, -4, -4, 4, 0, -4, -2, 0, 4, -2, -4, 2, 0, 0, 0, 4, 4, -2, -6, 2, 0, -6, 2, 2, 8, 0, -4, 2, 0, 0, 0, 2, 2, -6, -4, 2, 0, -2, 0, 4, 4, 0, -6, 2, -2, -2, 0, 0, 8, -4, -4, 2, -2, -4, 0, 2, 4, 0, -2, 2, 0, 0, 2, 4, 4, -2, -8, 2, 0, -6, 0, 2
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
FORMULA
|
G.f.: 1 + 2 * Sum_{k>0} (-1)^k * x^(k*(3*k+1)/2) * (1 + x^k) / (1 + x^(2*k)).
G.f.: ( Product_{k>0} 1-x^k ) * ( 1 + Sum_{k>0} x^k^2 / ((1+x^2)(1+x^4)...(1+x^(2k))) ).
|
|
PROGRAM
|
(PARI) {a(n) = if( n<0, 0, polcoeff( 1 + 2 * sum(k=1, (sqrtint(24*n+1) - 1) \ 6, (-1)^k * x^(k*(3*k+1)/2) * (1 + x^k) / (1 + x^(2*k)), x * O(x^n)), n))}
(PARI) {a(n) = local(t); if( n<0, 0, t = 1 + O(x^n); polcoeff( sum(k=1, sqrtint(n), t *= x^(2*k-1) / (1 + x^(2*k)) +O(x^(n-(k-1)^2+1)), 1) * eta(x + x*O(x^n)), n))}
|
|
CROSSREFS
|
Convolution of A053250 and A010815.
Sequence in context: A037868 A059963 A137934 this_sequence A111409 A125088 A027360
Adjacent sequences: A133735 A133736 A133737 this_sequence A133739 A133740 A133741
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Sep 22 2007
|
|
|
Search completed in 0.002 seconds
|
