|
Search: id:A005895
|
|
|
| A005895 |
|
Weighted count of partitions with distinct parts.
(Formerly M1337)
|
|
+0
4
|
|
| 1, 2, 5, 7, 12, 18, 26, 35, 50, 67, 88, 116, 149, 191, 245, 306, 381, 477, 585, 718, 880, 1067, 1288, 1555, 1863, 2226, 2656, 3151, 3726, 4406, 5180, 6077, 7124, 8316, 9691, 11278, 13080, 15146, 17517, 20204, 23264, 26759, 30705, 35182, 40274, 46000
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Also sum of largest parts of all partitions of n into distinct parts. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 15 2004
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Andrews, George E.; Ramanujan's "lost" notebook. V. Euler's partition identity. Adv. in Math. 61 (1986), no. 2, 156-164.
S.-Y. Kang, Generalizations of Ramanujan's reciprocity theorem..., J. London Math. Soc., 75 (2007), 18-34. See Eq. (1.5) but beware errors.
|
|
FORMULA
|
G.f.: Sum_{n=0..inf} {S(q)-(1+q)(1+q^2)...(1+q^n)}, where S(q) = g.f. for A000009.
|
|
MAPLE
|
M:=201; add( mul( (1+q^j), j=1..M) - mul( (1+q^j), j=1..n), n=0..M);
|
|
CROSSREFS
|
Cf. A005896, A003406.
Sequence in context: A024924 A023668 A023564 this_sequence A135525 A117538 A001060
Adjacent sequences: A005892 A005893 A005894 this_sequence A005896 A005897 A005898
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com) and Simon Plouffe (simon.plouffe(AT)gmail.com)
|
|
EXTENSIONS
|
More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 24 1999
|
|
|
Search completed in 0.002 seconds
|
