This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a003128 n = a003128_list !! n
a003128_list = zipWith3 (\x y z -> (x - 3 * y + z) `div` 2)
a000110_list (tail a000110_list) (drop 2 a000110_list)
-- Reinhard Zumkeller, Jun 30 2013
[(Bell(n) - 3*Bell(n+1) + Bell(n+2))/2: n in [0..30]]; // Vincenzo Librandi, Sep 19 2014
with(combinat); A000110:=n->sum(stirling2(n, k), k=0..n): f:=n->(A000110(n)-3*A000110(n+1)+A000110(n+2))/2;
a[n_] := (BellB[n] - 3*BellB[n+1] + BellB[n+2])/2; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jul 12 2012, after Vladeta Jovovic *)
max = 23; CoefficientList[ Series[1/2*(E^x - 1)^2*E^(E^x - 1), {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Oct 04 2013, after e.g.f. *)
makelist((belln(n)-3*belln(n+1)+belln(n+2))/2,n,0,23); /* Emanuele Munarini, Jul 14 2011 */
a(n)=sum(k=1,n,binomial(k,2)*stirling(n,k,2)) \\ Charles R Greathouse IV, Feb 07 2017
# Python 3.2 or higher required from itertools import accumulate A003128_list, blist, a, b = [], [1], 1, 1 for _ in range(30): blist = list(accumulate([b]+blist)) c = blist[-1] A003128_list.append((c+a-3*b)//2) a, b = b, c # Chai Wah Wu, Sep 19 2014
def A003128(n): return (bell_number(n) - 3*bell_number(n+1) + bell_number(n+2))/2 [A003128(n) for n in range(40)] # G. C. Greubel, Nov 04 2022
max = 18; CoefficientList[ Series[1/4*E^x*(E^(4*x) - 1)*E^((1/2)*(E^(2*x) - 1)), {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Oct 04 2013, after e.g.f. *)
x='x+O('x^66); concat([0], Vec( serlaplace( 1/4*(exp(4*x)-1)*exp(1/2*exp(2*x)+x-1/2) ) ) ) \\ Joerg Arndt, Oct 04 2013
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