A217144 - OEIS

%I #12 Jun 22 2022 14:49:41

%S 1,0,4,21,204,2500,38709,730420,16409180,430786429,13019414196,

%T 447437830704,17306961847705,746907935199264,35695643204860420,

%U 1876878693983656605,107956500727342113004,6758630146906528885412,458470139353155531447869

%N Alternating sums of squares of Bell numbers (A000110).

%F a(n) = Sum_{k=0..n} (-1)^(n-k)*Bell(k)^2.

%o (Maxima) makelist(sum((-1)^(n-k)*belln(k)^2,k,0,n),n,0,30);

%o (Python)

%o from itertools import accumulate, islice

%o def A217144_gen(): # generator of terms

%o     yield 1

%o     blist, b, c, f = (1,), 1, 1, 1

%o     while True:

%o         blist = list(accumulate(blist, initial=(b:=blist[-1])))

%o         yield (f:=-f)*(c := c+f*b**2)

%o A217144_list = list(islice(A217144_gen(),20)) # _Chai Wah Wu_, Jun 22 2022

%Y Cf. A000110, A005001, A087650, A217143.

%K nonn

%O 0,3

%A _Emanuele Munarini_, Sep 27 2012