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%I #20 Sep 08 2022 08:45:05
%S 1,1,15,21147,10480142147,4638590332229999353,
%T 3819714729894818339975525681317,
%U 10726137154573358400342215518590002633917247281
%N a(n) = Bell(n^2), where Bell(n) are the Bell numbers, cf. A000110.
%H Vincenzo Librandi, <a href="/A068939/b068939.txt">Table of n, a(n) for n = 0..20</a>
%F a(n) = exp(-1)*Sum(k=>0, k^(n^2)/k!). - _Benoit Cloitre_, May 19 2002
%F Integral representation as n-th moment of a positive function on a positive half-axis, in Maple notation: a(n)=int(x^n*(sum(exp(-ln(x)^2/ (4*ln(k)))/(k!*sqrt(ln(k))), k=2..infinity)/ (2*exp(1)*sqrt(Pi)*x) +Dirac(1-x)/exp(1)), x=0..infinity), n=0, 1, ...
%t Table[BellB[n^2], {n, 0, 8}] (* _Vincenzo Librandi_, Jul 16 2013 *)
%o (PARI) for(n=0,50,print1(round(sum(i=0,1000,i^(n^2)/(i)!)/exp(1)),","))
%o (Magma) [Bell(n^2): n in [0..8]]; // _Vincenzo Librandi_, Jul 16 2013
%o (Python)
%o from sympy import bell
%o def A068939(n): return bell(n**2) # _Chai Wah Wu_, Jun 22 2022
%Y Cf. A000110.
%K nonn
%O 0,3
%A _Karol A. Penson_, Mar 08 2002
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