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A308631
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Related to the position of the smallest part in all compositions of n.
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0
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1, 2, 7, 15, 36, 80, 174, 371, 787, 1644, 3410, 7031, 14423, 29455, 59948, 121656, 246302, 497661, 1003864, 2022143, 4068597, 8178131, 16425116, 32965907, 66125958, 132577442, 265700195, 532313023, 1066152092
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OFFSET
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3,2
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LINKS
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Knopfmacher, Arnold; Munagi, Augustine O. Smallest parts in compositions, Kotsireas, Ilias S. (ed.) et al., Advances in combinatorics. 3rd Waterloo workshop on computer algebra (WWCA, W80) 2011, Waterloo, Canada, May 26-29, 2011. Berlin: Springer. 197-207 (2013), V'(z,1,1).
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FORMULA
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G.f.: (x-1)^2*sum_{j>=1} x^(2*j+1)/((1-x-x^j)*(1-x-x^(j+1))^2).
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MAPLE
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(z-1)^2*add(z^(2*j+1)/(1-z-z^j)/(z^(j+1)+z-1)^2, j=1..34) ;
taylor(%, z=0, 32) ;
gfun[seriestolist](%) ;
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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