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A247452
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a(n)=3^n*Bell(n).
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8
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1, 3, 18, 135, 1215, 12636, 147987, 1917999, 27162540, 416236401, 6848207775, 120206639790, 2239278203277, 44074161731151, 913065539247018, 19843943547060315, 451135755042249987, 10701182793462338052, 264250529777677991751, 6779171511882363638619, 180350988089950776032172
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OFFSET
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0,2
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LINKS
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FORMULA
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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
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MATHEMATICA
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PROG
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(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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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