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, 1634675406, 2410208053, 3490696936, 4973757384, 6981792475, 9666797101, 13215829563, 17857209916

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

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).

Formula

a(n) = (n^8 - 8*n^7 + 36*n^6 - 92*n^5 + 155*n^4 - 148*n^3 + 88*n^2 - 16*n)/16.

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

Extensions

a(21) onward from Andrew Howroyd, Nov 09 2025

Status

approved