|
| |
|
|
A002512
|
|
Expansion of a modular function.
(Formerly M1380 N0539)
|
|
0
| |
|
|
1, 2, 5, 10, 22, 40, 75, 130, 230, 382, 636, 1022, 1645, 2570, 4002, 6110, 9297, 13910, 20715, 30462, 44597, 64584, 93085, 132990, 189164, 266992, 375192, 523800, 728285, 1006684, 1386043, 1898586, 2591120, 3519840, 4764736, 6423032
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| Newman, Morris; Construction and application of a class of modular functions. II. Proc. London Math. Soc. (3) 9 1959 373-387.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
FORMULA
| G.f.: Product ( 1 - x^k )^(-c(k)); c(k) = 2, 2, 2, 4, 2, 2, 2, 4, ....
Expansion of q^(5/12)/(eta(q)eta(q^4))^2 in powers of q.
Euler transform of period 4 sequence [2, 2, 2, 4, ...]. - Michael Somos Nov 10 2005
|
|
|
PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x+A)*eta(x^4+A))^-2, n))} /* Michael Somos Nov 10 2005 */
|
|
|
CROSSREFS
| Sequence in context: A110744 A079342 A034456 * A097096 A073777 A026633
Adjacent sequences: A002509 A002510 A002511 * A002513 A002514 A002515
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
|
| |
|
|
