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A276506
E.g.f.: exp(9*(exp(x)-1)).
3
1, 9, 90, 981, 11511, 144108, 1911771, 26730981, 392209380, 6016681467, 96202473183, 1599000785730, 27563715220509, 491777630207037, 9064781481234546, 172346601006842337, 3375007346801025099, 67983454804021156548, 1406921223577401454239, 29881379179971835132761
OFFSET
0,2
COMMENTS
Number of ways of placing n labeled balls into n unlabeled (but 9-colored) boxes.
LINKS
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.
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}]
PROG
(PARI) my(x='x+O('x^99)); Vec(serlaplace(exp(9*(exp(x)-1)))) \\ Altug Alkan, Sep 17 2016
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).
Sequence in context: A233829 A165324 A082367 * A049389 A127769 A276961
KEYWORD
nonn
AUTHOR
Vincenzo Librandi, Sep 17 2016
STATUS
approved