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A077045
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Doubly restricted composition numbers: number of compositions of 1+2+3+...+n=n(n+1)/2 into exactly n positive integers each no more than n.
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4
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1, 1, 2, 7, 44, 381, 4332, 60691, 1012664, 19610233, 432457640, 10701243741, 293661065788, 8851373201919, 290711372717976, 10334165623697259, 395320344293410544, 16192709833199300337, 707125993042984343136
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index entries for sequences related to compositions
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FORMULA
| a(n) =A077042(n, n). Roughly n^(n-3/2)*sqrt(6/pi) by the central limit theorem and something like n^n*sqrt(6/(pi*(n^3+0.3*n^2-0.91*n+0.3)) seems to be even closer.
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EXAMPLE
| a(3)=7 since the compositions of 1+2+3=6 into exactly 3 positive integers each no more than 3 are: 1+2+3, 1+3+2, 2+1+3, 2+2+2, 2+3+1, 3+1+2, 3+2+1.
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CROSSREFS
| Cf. A077042, A077046, A077047, A077048.
Sequence in context: A145073 A111561 A000155 * A178012 A194018 A196793
Adjacent sequences: A077042 A077043 A077044 * A077046 A077047 A077048
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KEYWORD
| nice,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Oct 22 2002
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