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 A247452 a(n)=3^n*Bell(n). 3
 1, 3, 18, 135, 1215, 12636, 147987, 1917999, 27162540, 416236401, 6848207775, 120206639790, 2239278203277, 44074161731151, 913065539247018, 19843943547060315, 451135755042249987, 10701182793462338052, 264250529777677991751, 6779171511882363638619, 180350988089950776032172 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Chai Wah Wu, Table of n, a(n) for n = 0..200 FORMULA a(n) = 3^n*A000110(n). a(n) = sum(k>=0, (3*k)^n/k!)/exp(1), this is a Dobinski-type formula. O.g.f.: sum(k>=0, 1/(k!*(1-3*k*z)) )/exp(1). E.g.f.: exp(exp(3*z)-1). 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)=sum(k>=0, Dirac(x-3*k)/k!)/exp(1). G.f.: 1/(1-3x/(1-3x/(1-3x/(1-6x/(1-3x/(1-9x/(1-...)...) (continued fraction). - Philippe Deléham, Sep 18 2014 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * 3^k * a(n-k). - Ilya Gutkovskiy, Jan 16 2020 MATHEMATICA Table[3^n BellB[n], {n, 0, 20}] (* Vincenzo Librandi, Sep 19 2014 *) PROG (Python) # Python 3.2 or above required. from itertools import accumulate A247452_list, blist, b, n3 = [1, 3], [1], 1, 9 for _ in range(2, 201): ....blist = list(accumulate([b]+blist)) ....b = blist[-1] ....A247452_list.append(b*n3) ....n3 *= 3 # Chai Wah Wu, Sep 19 2014 (MAGMA) [3^n*Bell(n): n in [0..20]]; // Vincenzo Librandi, Sep 19 2014 CROSSREFS Cf. A000110, A055882. Sequence in context: A151383 A177406 A289430 * A118970 A003122 A275549 Adjacent sequences:  A247449 A247450 A247451 * A247453 A247454 A247455 KEYWORD nonn AUTHOR Karol A. Penson, Sep 17 2014 STATUS approved

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Last modified February 23 21:20 EST 2020. Contains 332195 sequences. (Running on oeis4.)