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A105039
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Number of compositions of n with unique smallest part.
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1
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1, 1, 3, 3, 8, 11, 20, 34, 59, 96, 167, 282, 475, 800, 1352, 2275, 3828, 6426, 10785, 18085, 30297, 50698, 84770, 141623, 236425, 394381, 657380, 1094975, 1822628, 3031843, 5040129, 8373594, 13903588, 23072567, 38267330, 63435438, 105103059
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| G.f.: Sum(k*x^(2*k-1)/((1-x^k)*(1-x)^(k-1)), k=1..infinity).
Also (1-x)^2*Sum(x^k/(1-x-x^(k+1))^2, k=1..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 05 2005
a(n) = 1 + sum(k=2..[(n+3)/2], k * sum(s=1..[(n-1)/k], binomial(n-k*s-1, k-2) ) ) - Max Alekseyev (maxale(AT)gmail.com), Apr 15 2005
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EXAMPLE
| a(5)=8 because we have 5,14,41,23,32,122,212 and 221.
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MAPLE
| G:=sum(k*x^(2*k-1)/((1-x^k)*(1-x)^(k-1)), k=1..70):Gser:=series(G, x=0, 44):seq(coeff(Gser, x^n), n=1..41); (Deutsch)
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PROG
| (PARI) a(n)=1+sum(k=2, (n+3)\2, k*sum(s=1, (n-1)\k, binomial(n-k*s-1, k-2))) (Alekseyev)
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CROSSREFS
| Cf. A079501, A097979.
Sequence in context: A141577 A123315 A052407 * A090597 A126073 A126592
Adjacent sequences: A105036 A105037 A105038 * A105040 A105041 A105042
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 03 2005
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Max Alekseyev (maxale(AT)gmail.com), Apr 13 2005
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