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Search: id:A104383
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| A104383 |
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Number of distinct partitions of triangular numbers n*(n+1)/2. |
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+0
3
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| 1, 2, 4, 10, 27, 76, 222, 668, 2048, 6378, 20132, 64234, 206848, 671418, 2194432, 7215644, 23853318, 79229676, 264288462, 884987529, 2973772212, 10024300890, 33888946600, 114872472064, 390334057172, 1329347719190, 4536808055808
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Equals row sums of triangle A104382. Asymptotics: a(n) ~ exp(Pi*sqrt((n^2+n)/6))/(2*6^(1/4))/(n^2+n)^(3/4).
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REFERENCES
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Abramowitz, M. and Stegun, I. A. (Eds.). "Partitions into Distinct Parts." S24.2.2 in Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, 9th printing. New York: Dover, pp. 825-826, 1972.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Eric Weisstein's World of Mathematics, Partition Function Q.
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FORMULA
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Limit_{n-->inf} a(n+1)/a(n) = exp(sqrt(Pi^2/6)) = 3.605822247984...
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PROGRAM
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(PARI) {a(n)=polcoeff(prod(k=1, n*(n+1)/2, 1+x^k, 1+x*O(x^(n*(n+1)/2))), n*(n+1)/2)}
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CROSSREFS
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Cf. A000009, A104382.
Sequence in context: A086991 A113066 A002459 this_sequence A108523 A157003 A114507
Adjacent sequences: A104380 A104381 A104382 this_sequence A104384 A104385 A104386
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 04 2005
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