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%I #18 Jun 02 2019 14:07:00
%S 0,5,5,65,205,1405,7425,44385,271205,1666925,10312945,63728065,
%T 389047365,2328509565,13621340225,77892637505,436228078405,
%U 2398628051245,12982985597745,69342874061025,366249017075045,1916461175393405,9950645526554305,51333364246248865
%N Number of n-digit numbers m such that (a) the digits of m are from the set {1, 2, 3, 4, 5}, (b) any digit that appears in m appears at least twice.
%C All numbers are divisible by 5.
%F E.g.f.: (exp(x) - x)^5. - _Geoffrey Critzer_, Jan 29 2015
%e a(1)=0 trivially.
%e a(2)=5 because there are 5 eligible numbers 11, 22, 33, 44, 55.
%e a(3)=5 because there are 5 eligible numbers 111, 222, 333, 444, 555.
%e a(4)=65 because there are 65 eligible numbers:
%e 1111,1122,1133,1144,1155,1212,1221,1313,1331,1414,1441,1515,1551,
%e 2112,2121,2211,2222,2233,2244,2255,2323,2332,2424,2442,2525,2552,
%e 3113,3131,3223,3232,3311,3322,3333,3344,3355,3434,3443,3535,3553,
%e 4114,4141,4224,4242,4334,4343,4411,4422,4433,4444,4455,4545,4554,
%e 5115,5151,5225,5252,5335,5353,5445,5454,5511,5522,5533,5544,5555.
%t nn = 20; Rest[Range[0, nn]! CoefficientList[Series[(Exp[x] - x)^5, {x,0,nn}], x]] (* _Geoffrey Critzer_, Jan 29 2015 *)
%Y Cf. A171725 (n=6 case).
%K base,nonn
%O 1,2
%A _Zak Seidov_, Dec 16 2009
%E More terms from _Geoffrey Critzer_, Jan 29 2015