|
Search: id:A005758
|
|
|
| A005758 |
|
Coefficients of modular function g_5(tau) (partitions of n into parts of 12 kinds).
(Formerly M4854)
|
|
+0
4
|
|
| 1, 12, 90, 520, 2535, 10908, 42614, 153960, 521235, 1669720, 5098938, 14931072, 42124380, 114945780, 304351020, 784087848, 1970043621, 4837060800, 11626305640, 27398234760, 63388751544, 144156086776, 322590526350
(list; graph; listen)
|
|
|
OFFSET
|
5,2
|
|
|
COMMENT
|
a(n-5) is Euler transform of A010851. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
Convolution square of A005758 = A006922: (1, 24, 324, 3200, 25650,...) [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009]
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glasgow Math. J., 8 (1967), 14-32.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=5..205
Index entries for expansions of Product_{k >= 1} (1-x^k)^m
N. J. A. Sloane, Transforms [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
|
|
FORMULA
|
G.f.: Product ( 1 - x^k )^(-12).
|
|
MAPLE
|
with (numtheory): b:= proc(n) option remember; `if`(n=0, 1, add (add (d*12, d=divisors(j)) *b(n-j), j=1..n)/n) end: a:= n->b(n-5): seq (a(n), n=5..40); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
|
|
CROSSREFS
|
Cf. 12th column of A144064. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
A006922 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009]
Sequence in context: A034197 A156397 A121590 this_sequence A084485 A135158 A130072
Adjacent sequences: A005755 A005756 A005757 this_sequence A005759 A005760 A005761
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
|
|
|
Search completed in 0.002 seconds
|
