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A247452 a(n)=3^n*Bell(n). 2
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

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 November 18 15:55 EST 2018. Contains 317323 sequences. (Running on oeis4.)