A276506 E.g.f.: exp(9*(exp(x)-1)).

1, 9, 90, 981, 11511, 144108, 1911771, 26730981, 392209380, 6016681467, 96202473183, 1599000785730, 27563715220509, 491777630207037, 9064781481234546, 172346601006842337, 3375007346801025099, 67983454804021156548, 1406921223577401454239, 29881379179971835132761

Offset: 0

Author

Vincenzo Librandi, Sep 17 2016

Keywords

• nonn

Comments

Number of ways of placing n labeled balls into n unlabeled (but 9-colored) boxes.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..514

Crossrefs

Cf. similar sequences with e.g.f. exp(k*(exp(x)-1)): A001861 (k=2), A027710 (k=3), A078944 (k=4), A144180 (k=5) A144223 (k=6), A144263 (k=7), A221159 (k=8), this sequence (k=9), A276507 (k=10).

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      (1+add(binomial(n-1, k-1)*a(n-k), k=1..n-1))*9)
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Sep 25 2017

Mathematica

Table[BellB[n, 9], {n, 0, 30}]

PARI

my(x='x+O('x^99)); Vec(serlaplace(exp(9*(exp(x)-1)))) \\ Altug Alkan, Sep 17 2016

Formula

G.f.: A(x) satisfies 9*(x/(1-x))*A(x/(1-x)) = A(x)-1; nine times the binomial transform equals this sequence shifted one place left.