%I #17 Sep 09 2023 11:23:30
%S 1,10,136,2056,29246,376414,4366881,47111408,487875964,4951921240,
%T 49815780829,499304300676,4997363405880,49989815235610,
%U 499959437775564,4999832460244272,49999282163551040,499996822399017380,4999985554326500949,49999932964605448756,499999684083134646700,4999998493912339729030,49999992756990963293576,499999964931001199898296,4999999829289953917354596
%N Number of n-digit biquanimous numbers in base 10 allowing leading zeros.
%C A biquanimous number (A064544) is a number whose digits can be split into two groups with equal sums.
%D _William P. Thurston_, personal communication.
%H Alois P. Heinz, <a href="/A065024/b065024.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_29">Index entries for linear recurrences with constant coefficients</a>, signature (62, -1807, 33062, -427564, 4169600, -31932484, 197416064, -1004816182, 4272066348, -15337434186, 46879240956, -122734147260, 276448013616, -537280650948, 902485024560, -1310712845937, 1644560278758, -1778909274239, 1653055768558, -1312795678832, 884596325632, -500792236832, 235030416448, -89771423744, 27185833984, -6278031104, 1038269952, -109486080, 5529600).
%F G.f.: (2764800*x^35 -54743040*x^34 +535723776*x^33 -3484062592*x^32 +17047244288*x^31 -67056352000*x^30 +220043616032*x^29 -610136398384*x^28 +1428398369904*x^27 -2800237309450*x^26 +4555415187081*x^25 -6116515610358*x^24 +6790044899737*x^23 -6333177380214*x^22 +5196278284089*x^21 -4097957831766*x^20 +3395084470412*x^19 -2936902021347*x^18 +2431358755383*x^17 -1791957130479*x^16 +1141680065910*x^15 -626654334304*x^14 +298277671441*x^13 -124021600362*x^12 +45181016933*x^11 -14371192060*x^10 +3953830871*x^9 -928344574*x^8 +183129613*x^7 -29820446*x^6 +3925130*x^5 -406196*x^4 +31739*x^3 -1755*x^2 +61*x-1) / ((10*x-1) *(5*x-1) *(4*x-1)^2 *(3*x-1)^3 *(2*x-1)^8 *(x-1)^14). - _Alois P. Heinz_, Jun 12 2017
%F Limit_{n->oo} a(n)/10^n = 1/2. - _Stefano Spezia_, Sep 09 2023
%Y Cf. A064544, A065023, A065025, A065086.
%Y Column k=9 of A288638.
%K nonn,base,easy
%O 1,2
%A _N. J. A. Sloane_, Nov 03 2001