cp's OEIS Frontend

A157992 Number of n-colorings of the Dyck Graph.

%I A157992 #15 Feb 16 2025 08:33:09
%S A157992 0,0,2,15915138,20127046304340,528133663294428020,
%T A157992 1266096501642919005750,677034005092723101211542,
%U A157992 130523162841884328808537448,12040770257335491821696076840,636442821346312893265045966890,21766425371195465558485996323050
%N A157992 Number of n-colorings of the Dyck Graph.
%C A157992 The Dyck Graph has 32 nodes and 48 edges.
%H A157992 Alois P. Heinz, <a href="/A157992/b157992.txt">Table of n, a(n) for n = 0..1000</a>
%H A157992 Timme, Marc; van Bussel, Frank; Fliegner, Denny; Stolzenberg, Sebastian (2009) "Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions", New J. Phys. 11 023001, doi: <a href="http://dx.doi.org/10.1088/1367-2630/11/2/023001">10.1088/1367-2630/11/2/023001</a>.
%H A157992 Weisstein, Eric W. "<a href="https://mathworld.wolfram.com/DyckGraph.html">Dyck Graph</a>".
%H A157992 Weisstein, Eric W. "<a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>".
%H A157992 <a href="/index/Rec#order_33">Index entries for linear recurrences with constant coefficients</a>, signature (33, -528, 5456, -40920, 237336, -1107568, 4272048, -13884156, 38567100, -92561040, 193536720, -354817320, 573166440, -818809200, 1037158320, -1166803110, 1166803110, -1037158320, 818809200, -573166440, 354817320, -193536720, 92561040, -38567100, 13884156, -4272048, 1107568, -237336, 40920, -5456, 528, -33, 1).
%F A157992 a(n) = n^32 -48*n^31 + ... (see Maple program).
%p A157992 a:= n-> n^32 -48*n^31 +1128*n^30 -17296*n^29 +194580*n^28 -1712288*n^27 +12270824*n^26 -73614612*n^25 +377151046*n^24 -1675122096*n^23 +6525181008*n^22 -22496343408*n^21 +69142793916*n^20 -190544188160*n^19 +472961919106*n^18 -1061083039384*n^17 +2157059631081*n^16
%p A157992 -3979825893416*n^15 +6668841887020*n^14 -10145667663516*n^13 +13993265083448*n^12 -17447849898820*n^11 +19579417254232*n^10 -19643437430604*n^9 +17454210580012*n^8 -13554627923192*n^7 +9029110616240*n^6 -5021752293076*n^5 +2239517417991*n^4 -750356179848*n^3 +167614890262*n^2 -18665552131*n:
%p A157992 seq(a(n), n=0..30);
%K A157992 nonn,easy
%O A157992 0,3
%A A157992 _Alois P. Heinz_, Mar 10 2009