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A247452 a(n) = 3^n*Bell(n).

%I A247452 #58 May 17 2025 07:30:41
%S A247452 1,3,18,135,1215,12636,147987,1917999,27162540,416236401,6848207775,
%T A247452 120206639790,2239278203277,44074161731151,913065539247018,
%U A247452 19843943547060315,451135755042249987,10701182793462338052,264250529777677991751,6779171511882363638619,180350988089950776032172
%N A247452 a(n) = 3^n*Bell(n).
%H A247452 Chai Wah Wu, <a href="/A247452/b247452.txt">Table of n, a(n) for n = 0..200</a>
%F A247452 a(n) = 3^n*A000110(n).
%F A247452 a(n) = (1/e)*Sum_{k>=0} (3*k)^n/k!. (This is a Dobinski-type formula.)
%F A247452 O.g.f.: (1/e)*Sum_{k>=0} 1/(k!*(1-3*k*z)).
%F A247452 E.g.f.: exp(exp(3*z)-1).
%F A247452 a(n) is the n-th moment of a discrete, positive weight function w(x) consisting of an infinite comb of Dirac delta functions situated at x=3*k, with k = 0, 1, ..., defined as w(x) = (1/e)*Sum_{k>=0} Dirac(x-3*k)/k!.
%F A247452 G.f.: 1/(1-3*x/(1-3*x/(1-3*x/(1-6*x/(1-3*x/(1-9*x/(1-...))))))) (continued fraction). - _Philippe Deléham_, Sep 18 2014
%F A247452 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * 3^k * a(n-k). - _Ilya Gutkovskiy_, Jan 16 2020
%t A247452 Table[3^n BellB[n], {n, 0, 20}] (* _Vincenzo Librandi_, Sep 19 2014 *)
%o A247452 (Python)
%o A247452 # Python 3.2 or above required.
%o A247452 from itertools import accumulate
%o A247452 A247452_list, blist, b, n3 = [1,3], [1], 1, 9
%o A247452 for _ in range(2,201):
%o A247452     blist = list(accumulate([b]+blist))
%o A247452     b = blist[-1]
%o A247452     A247452_list.append(b*n3)
%o A247452     n3 *= 3 # _Chai Wah Wu_, Sep 19 2014
%o A247452 (Magma) [3^n*Bell(n): n in [0..20]]; // _Vincenzo Librandi_, Sep 19 2014
%Y A247452 Cf. A000110, A055882.
%K A247452 nonn
%O A247452 0,2
%A A247452 _Karol A. Penson_, Sep 17 2014