A265325 Number of n-digit decimal numbers with leading zeros allowed where no digit appears exactly twice.

10, 90, 730, 5410, 37900, 264250, 1908910, 14322520, 110305720, 875799550, 7203731050, 60866700940, 527138423380, 4696469283970, 42797376850150, 397903278667600, 3783002076771760, 36604891556846470, 360117919584474850, 3603555076712108500

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Math Stackexchange, Marko Riedel et al., N digit numbers with no digit appearing exactly twice.

Formula

E.g.f.: Sum_{q=1..N} C(10,q)*(exp(z)-z^2/2-1)^q.

E.g.f.: (exp(z)-z^2/2)^10.

Example

Computing the value for n=1 the ten one-digit numbers 0-9 all qualify.
Computing the value for n=2 of two-digit numbers 00-99 all qualify except those consisting of a double digit (00, 11, ..., 99).

Maple

STNE2 := (n, k)->n!*coeftayl((exp(z)-z^2/2-1)^k/k!, z=0, n);
a(N) := N -> add(combinat:-binomial(10, q)*STNE2(N, q)*q!, q = 1 .. N)

Mathematica

With[{nn=20}, Rest[CoefficientList[Series[(Exp[x]-x^2/2)^10, {x, 0, nn}], x] Range[0, nn]!]] (* Harvey P. Dale, Oct 07 2024 *)

Crossrefs

Cf. A272501, A272502, A272503.

Sequence in context: A319893 A319874 A159733 * A038726 A009454 A231530

Adjacent sequences: A265322 A265323 A265324 * A265326 A265327 A265328

Keyword

nonn,base

Author

Marko Riedel, Apr 30 2016

Status

approved