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A092319
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Sum of smallest parts of all partitions of n into odd distinct parts.
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3
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1, 0, 3, 1, 5, 1, 7, 4, 10, 4, 12, 9, 15, 9, 20, 17, 23, 17, 28, 27, 36, 28, 41, 43, 50, 44, 62, 62, 71, 66, 84, 91, 103, 96, 119, 127, 139, 137, 167, 178, 191, 192, 223, 241, 266, 264, 302, 331, 351, 360, 411, 439, 469, 485, 542, 587, 628, 646, 714, 773, 819, 854, 945
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n)=sum(A116860(n,k), k>=0). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2006
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FORMULA
| G.f.: Sum((2*n-1)*x^(2*n-1)*Product(1+x^(2*k+1), k = n .. infinity), n = 1 .. infinity).
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EXAMPLE
| a(13)=15 because the partitions of 13 into distinct odd parts are [13],[9,3,1] and [7,5,1], with sum of the smallest terms 13+1+1=15.
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MAPLE
| f:=sum((2*n-1)*x^(2*n-1)*product(1+x^(2*k+1), k=n..40), n=1..40): fser:=simplify(series(f, x=0, 66)): seq(coeff(fser, x^n), n=1..63); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2006
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CROSSREFS
| Cf. A092316.
Cf. A116860.
Sequence in context: A136180 A095112 A160596 * A147410 A146623 A197943
Adjacent sequences: A092316 A092317 A092318 * A092320 A092321 A092322
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 15 2004
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EXTENSIONS
| More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
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