A210766 Number of 8-hoops with n symbols and no a-rooted trees.

1, 13, 141, 1204, 7570, 36021, 136948, 436696, 1212399, 3013165, 6843991, 14431308, 28591576, 53726869, 96473910, 166535536, 277726093, 449264781, 707353489, 1087078180

Offset: 1

Author

N. J. A. Sloane, Mar 25 2012

Keywords

• nonn
• easy

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).
• Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Crossrefs

Cf. A060560, A210768, A295925.

Programs

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

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]