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%I #5 Jun 14 2017 10:15:51
%S 1,1,9,109,1457,18231,205837,2112384,20341201,189013501,1725377947,
%T 15622028115,140950202021,1269874954518,11433967343409,
%U 102926130336136,926421241593985,8338171770377449,75045297684511343,675415983886759045,6078784024809901485
%N Number of n-digit biquanimous strings using digits {0,1,...,8}.
%C A biquanimous string is a string whose digits can be split into two groups with equal sums.
%H Alois P. Heinz, <a href="/A288692/b288692.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (49, -1114, 15704, -154592, 1133720, -6448172, 29219972, -107498498, 325391618, -818066864, 1719218324, -3031985264, 4494756128, -5598534740, 5843651372, -5085390293, 3660194213, -2153194198, 1017730084, -376961752, 105342192, -20876832, 2614464, -155520).
%F G.f.: -(77760*x^29 -1384992*x^28 +12134448*x^27 -69723432*x^26 +294884564*x^25 -975139270*x^24 +2569875380*x^23 -5484438559*x^22 +9604318227*x^21 -13997308104*x^20 +17318565226*x^19 -18674789778*x^18 +18024625668*x^17 -15836546206*x^16 +12680214123*x^15 -9166750277*x^14 +5925087725*x^13 -3404858524*x^12 +1731743202*x^11 -773011544*x^10 +298459228*x^9 -97814317*x^8 +26669775*x^7 -5929660*x^6 +1052200*x^5 -145030*x^4 +14922*x^3 -1074*x^2 +48*x -1) / ((9*x-1) *(5*x-1) *(3*x-1)^3 *(2*x-1)^7 *(x-1)^12).
%Y Column k=8 of A288638.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Jun 13 2017
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