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A217143 Sum of squares of Bell numbers (A000110).

%I A217143 #19 Sep 08 2022 08:46:04
%S A217143 1,2,6,31,256,2960,44169,813298,17952898,465148507,13915349132,
%T A217143 474372594032,18228772272441,782443669319410,37224994809379094,
%U A217143 1949799331997896119,111783178753323665728,6978369826387194664144,472207139326449254997425
%N A217143 Sum of squares of Bell numbers (A000110).
%F A217143 a(n) = Sum_{k=0..n} Bell(k)^2.
%t A217143 Accumulate[BellB[Range[0, 20]]^2] (* _Bruno Berselli_, Sep 27 2012 *)
%o A217143 (Maxima) makelist(sum(belln(k)^2,k,0,n),n,0,30);
%o A217143 (Magma) [&+[Bell(i)^2: i in [0..n]]: n in [0..20]]; // _Bruno Berselli_, Sep 27 2012
%o A217143 (Python)
%o A217143 from itertools import accumulate, islice
%o A217143 def A217143_gen(): # generator of terms
%o A217143     yield 1
%o A217143     blist, b, c = (1,), 1, 1
%o A217143     while True:
%o A217143         blist = list(accumulate(blist, initial=(b:=blist[-1])))
%o A217143         yield (c := c+b**2)
%o A217143 A217143_list = list(islice(A217143_gen(),20)) # _Chai Wah Wu_, Jun 22 2022
%Y A217143 Cf. A000110, A005001, A087650, A217144.
%Y A217143 Partial sums of A001247.
%K A217143 nonn
%O A217143 0,2
%A A217143 _Emanuele Munarini_, Sep 27 2012