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 A210766 Number of 8-hoops with n symbols and no a-rooted trees. 4
 1, 13, 141, 1204, 7570, 36021, 136948, 436696, 1212399, 3013165, 6843991, 14431308, 28591576, 53726869, 96473910, 166535536, 277726093, 449264781, 707353489, 1087078180 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS S. G. Williamson, The combinatorial analysis of patterns and the principle of inclusion-exclusion, Discrete Math. 1 (1972), no. 4, 357--388. MR0299493 (45 #8541). FORMULA G.f.: x*(1+x)*(1+3*x+57*x^2+262*x^3+582*x^4+321*x^5+34*x^6)/(1-x)^9. [Colin Barker, Apr 17 2012] MAPLE A210766 := proc(n) (n^8-8*n^7+36*n^6-92*n^5+155*n^4-148*n^3 +88*n^2-16*n)/16 ; end proc: # R. J. Mathar, Mar 27 2012 CROSSREFS Cf. A060560, A210768, A295925. Sequence in context: A138931 A157160 A263480 * A045742 A122011 A221103 Adjacent sequences: A210763 A210764 A210765 * A210767 A210768 A210769 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Mar 25 2012 STATUS approved

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Last modified November 27 22:56 EST 2022. Contains 358406 sequences. (Running on oeis4.)