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Baym, Blaizot, and Zinn-Justin have recently used the large N approximationto calculate the effect of interactions on the transition temperature of diluteBose gases. We extend their calculation to next-to-leading-order in 1/N andfind a relatively small correction of -26% to the leading-order result. Thissuggests that the large N approximation works surprisingly well in thisapplication.Comment: 21 pages, 7+1 figures; an embarassing factor of 2 has been corrected  in the evaluation of one diagram, changing the previous +18% result for the  NLO correction to -26

T_{c} for dilute Bose gases: Beyond leading order in 1/N