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, 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.

Links

Table of n, a(n) for n=1..24.

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

Adjacent sequences: A171723 A171724 A171725 * A171727 A171728 A171729

Keyword

base,nonn

Author

Zak Seidov, Dec 16 2009

Extensions

More terms from Geoffrey Critzer, Jan 29 2015

Status

approved