|
Search: id:A137829
|
|
|
| A137829 |
|
Expansion of psi(q^2) / f(-q)^2 in powers of q where psi(), f() are Ramanujan theta functions. |
|
+0
3
|
|
| 1, 2, 6, 12, 25, 46, 86, 148, 255, 420, 686, 1088, 1712, 2634, 4020, 6036, 8988, 13214, 19282, 27840, 39923, 56750, 80160, 112384, 156660, 216958, 298894, 409420, 558119, 756950, 1022090, 1373760, 1838932, 2451366, 3255480, 4306920, 5678104
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
FORMULA
|
Expansion of q^(-1/6) * eta(q^4)^2 / (eta(q)^2 * eta(q^2)) in powers of q.
Euler transform of period 4 sequence [ 2, 3, 2, 1, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (72 t)) = 96^(-1/2) (t/i)^(-1/2) g(t) where q = exp(2 pi i t) and g(t) is g.f. for A137830.
G.f.: Product_{k>0} (1 + x^k) * (1 + x^(2*k))^2 / (1 - x^k).
|
|
EXAMPLE
|
q + 2*q^7 + 6*q^13 + 12*q^19 + 25*q^25 + 46*q^31 + 86*q^37 + 148*q^43 + ...
|
|
PROGRAM
|
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^2 / eta(x + A)^2 / eta(x^2 + A), n))}
|
|
CROSSREFS
|
A137828(4*n+1) = 2 * a(n).
Sequence in context: A163264 A163895 A034882 this_sequence A045925 A128020 A116562
Adjacent sequences: A137826 A137827 A137828 this_sequence A137830 A137831 A137832
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Michael Somos, Feb 12 2008
|
|
|
Search completed in 0.002 seconds
|
