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A171726
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.
0
0, 5, 5, 65, 205, 1405, 7425, 44385, 271205, 1666925, 10312945, 63728065, 389047365, 2328509565, 13621340225, 77892637505, 436228078405, 2398628051245, 12982985597745, 69342874061025, 366249017075045, 1916461175393405, 9950645526554305, 51333364246248865
OFFSET
1,2
COMMENTS
All numbers are divisible by 5.
FORMULA
E.g.f.: (exp(x) - x)^5. - Geoffrey Critzer, Jan 29 2015
EXAMPLE
a(1)=0 trivially.
a(2)=5 because there are 5 eligible numbers 11, 22, 33, 44, 55.
a(3)=5 because there are 5 eligible numbers 111, 222, 333, 444, 555.
a(4)=65 because there are 65 eligible numbers:
1111,1122,1133,1144,1155,1212,1221,1313,1331,1414,1441,1515,1551,
2112,2121,2211,2222,2233,2244,2255,2323,2332,2424,2442,2525,2552,
3113,3131,3223,3232,3311,3322,3333,3344,3355,3434,3443,3535,3553,
4114,4141,4224,4242,4334,4343,4411,4422,4433,4444,4455,4545,4554,
5115,5151,5225,5252,5335,5353,5445,5454,5511,5522,5533,5544,5555.
MATHEMATICA
nn = 20; Rest[Range[0, nn]! CoefficientList[Series[(Exp[x] - x)^5, {x, 0, nn}], x]] (* Geoffrey Critzer, Jan 29 2015 *)
CROSSREFS
Cf. A171725 (n=6 case).
Sequence in context: A009334 A151467 A241209 * A129358 A318420 A151492
KEYWORD
base,nonn
AUTHOR
Zak Seidov, Dec 16 2009
EXTENSIONS
More terms from Geoffrey Critzer, Jan 29 2015
STATUS
approved