|
Search: id:A005896
|
|
|
| A005896 |
|
Weighted count of partitions with odd parts.
(Formerly M2338)
|
|
+0
3
|
|
| 0, 0, 0, 1, 1, 3, 4, 7, 9, 14, 19, 26, 34, 45, 59, 76, 96, 121, 153, 189, 234, 288, 353, 428, 519, 625, 752, 900, 1073, 1274, 1512, 1784, 2101, 2470, 2894, 3382, 3946, 4590, 5330, 6179, 7144, 8246, 9505, 10931, 12552, 14396, 16476, 18831, 21495
(list; graph; listen)
|
|
|
OFFSET
|
0,6
|
|
|
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.
|
|
FORMULA
|
G.f.: Sum_{n=0..inf} {S(q)-1/((1-q)(1-q^3)...(1-q^(2n+1)))}, where S(q) = g.f. for A000009.
|
|
PROGRAM
|
(PARI) /* set "infinity" */ oo = 50; /* G.f. for partitions with odd parts: */ Q(n, q) = prod(k=0, n, 1/(1-q^(2*k+1)), 1+q*O(q^oo)); /* G.f. for A000009: */ Sq = Q(oo/2, q); /* G.f. for A005896: */ Sq0 = sum(n=0, oo/2, Sq-Q(n, q)); for(n=0, 48, print1(polcoeff(Sq0, n)", "))
|
|
CROSSREFS
|
Cf. A000009, A005895, A003406.
Sequence in context: A140208 A098390 A008763 this_sequence A147953 A163468 A069183
Adjacent sequences: A005893 A005894 A005895 this_sequence A005897 A005898 A005899
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
|
|
EXTENSIONS
|
More terms from Michael Somos.
|
|
|
Search completed in 0.004 seconds
|
