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%I A217144 #12 Jun 22 2022 14:49:41
%S A217144 1,0,4,21,204,2500,38709,730420,16409180,430786429,13019414196,
%T A217144 447437830704,17306961847705,746907935199264,35695643204860420,
%U A217144 1876878693983656605,107956500727342113004,6758630146906528885412,458470139353155531447869
%N A217144 Alternating sums of squares of Bell numbers (A000110).
%F A217144 a(n) = Sum_{k=0..n} (-1)^(n-k)*Bell(k)^2.
%o A217144 (Maxima) makelist(sum((-1)^(n-k)*belln(k)^2,k,0,n),n,0,30);
%o A217144 (Python)
%o A217144 from itertools import accumulate, islice
%o A217144 def A217144_gen(): # generator of terms
%o A217144     yield 1
%o A217144     blist, b, c, f = (1,), 1, 1, 1
%o A217144     while True:
%o A217144         blist = list(accumulate(blist, initial=(b:=blist[-1])))
%o A217144         yield (f:=-f)*(c := c+f*b**2)
%o A217144 A217144_list = list(islice(A217144_gen(),20)) # _Chai Wah Wu_, Jun 22 2022
%Y A217144 Cf. A000110, A005001, A087650, A217143.
%K A217144 nonn
%O A217144 0,3
%A A217144 _Emanuele Munarini_, Sep 27 2012

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