G.f.: (1+2097144*x+154082187*x^2+1186203088*x^3+1961635263*x^4+785850072*x^5+ 60509029*x^6+279936*x^7)/(-1+x)^8 . [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 24 2009]
PROG
(MAGMA) [(7*n+1)^7: n in [0..20]]; // Vincenzo Librandi, Jul 13 2011