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%I #30 Jul 27 2021 11:29:08
%S 1,9,90,981,11511,144108,1911771,26730981,392209380,6016681467,
%T 96202473183,1599000785730,27563715220509,491777630207037,
%U 9064781481234546,172346601006842337,3375007346801025099,67983454804021156548,1406921223577401454239,29881379179971835132761
%N E.g.f.: exp(9*(exp(x)-1)).
%C Number of ways of placing n labeled balls into n unlabeled (but 9-colored) boxes.
%H Alois P. Heinz, <a href="/A276506/b276506.txt">Table of n, a(n) for n = 0..514</a>
%F 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.
%p a:= proc(n) option remember; `if`(n=0, 1,
%p (1+add(binomial(n-1, k-1)*a(n-k), k=1..n-1))*9)
%p end:
%p seq(a(n), n=0..25); # _Alois P. Heinz_, Sep 25 2017
%t Table[BellB[n, 9], {n, 0, 30}]
%o (PARI) my(x='x+O('x^99)); Vec(serlaplace(exp(9*(exp(x)-1)))) \\ _Altug Alkan_, Sep 17 2016
%Y 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).
%K nonn
%O 0,2
%A _Vincenzo Librandi_, Sep 17 2016