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A213289 Number of 10-length words w over n-ary alphabet such that for every prefix z of w we have #(z,a_i) = 0 or #(z,a_i) >= #(z,a_j) for all j>i and #(z,a_i) counts the occurrences of the i-th letter in z.

%I A213289 #14 Jun 13 2015 00:54:16
%S A213289 0,1,323,5168,37993,201975,916966,3771418,14486158,52359693,178880725,
%T A213289 575581556,1731294863,4845394723,12619979568,30703918750,70168864396,
%U A213289 151545355033,311129635863,610492421368,1150383157925,2090531036111,3677200683178,6280769764578
%N A213289 Number of 10-length words w over n-ary alphabet such that for every prefix z of w we have #(z,a_i) = 0 or #(z,a_i) >= #(z,a_j) for all j>i and #(z,a_i) counts the occurrences of the i-th letter in z.
%H A213289 Alois P. Heinz, <a href="/A213289/b213289.txt">Table of n, a(n) for n = 0..1000</a>
%H A213289 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F A213289 a(n) = n*(-6044030 +17209877*n -19851310*n^2 +12422410*n^3 -4715472*n^4 +1139127*n^5 -176832*n^6 +17190*n^7 -960*n^8 +24*n^9)/24.
%F A213289 G.f.: x*(1+312*x +1670*x^2 -1255*x^3 +15327*x^4 +38264*x^5 +81248*x^6 +406785*x^7 +520730*x^8 +2565718*x^9)/(1-x)^11.
%e A213289 a(0) = 0: no word of length 10 is possible for an empty alphabet.
%e A213289 a(1) = 1: aaaaaaaaaa for alphabet {a}.
%e A213289 a(2) = 323: aaaaaaaaaa, aaaaaaaaab, ..., baabababab, bbbbbbbbbb for alphabet {a,b}.
%p A213289 a:= n-> n*(-6044030+ (17209877+ (-19851310+ (12422410+ (-4715472+ (1139127+ (-176832+ (17190+(-960+24*n) *n)*n)*n)*n)*n)*n)*n)*n)/24:
%p A213289 seq(a(n), n=0..40);
%Y A213289 Row n=10 of A213276.
%K A213289 nonn,easy
%O A213289 0,3
%A A213289 _Alois P. Heinz_, Jun 08 2012