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Search: id:A005896
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| A005896 |
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Weighted count of partitions with odd parts.
(Formerly M2338)
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+0
3
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| 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)
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OFFSET
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0,6
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REFERENCES
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Andrews, George E. Ramanujan's "lost" notebook. V. Euler's partition identity. Adv. in Math. 61 (1986), no. 2, 156-164.
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FORMULA
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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.
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PROGRAM
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(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)", "))
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CROSSREFS
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Cf. A000009, A005895, A003406.
Adjacent sequences: A005893 A005894 A005895 this_sequence A005897 A005898 A005899
Sequence in context: A140208 A098390 A008763 this_sequence A069183 A119907 A086772
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
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EXTENSIONS
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More terms from Michael Somos.
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