A217143 Sum of squares of Bell numbers (A000110).
1, 2, 6, 31, 256, 2960, 44169, 813298, 17952898, 465148507, 13915349132, 474372594032, 18228772272441, 782443669319410, 37224994809379094, 1949799331997896119, 111783178753323665728, 6978369826387194664144, 472207139326449254997425
Offset: 0
Keywords
Programs
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Magma
[&+[Bell(i)^2: i in [0..n]]: n in [0..20]]; // Bruno Berselli, Sep 27 2012
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Mathematica
Accumulate[BellB[Range[0, 20]]^2] (* Bruno Berselli, Sep 27 2012 *)
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Maxima
makelist(sum(belln(k)^2,k,0,n),n,0,30);
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Python
from itertools import accumulate, islice def A217143_gen(): # generator of terms yield 1 blist, b, c = (1,), 1, 1 while True: blist = list(accumulate(blist, initial=(b:=blist[-1]))) yield (c := c+b**2) A217143_list = list(islice(A217143_gen(),20)) # Chai Wah Wu, Jun 22 2022
Formula
a(n) = Sum_{k=0..n} Bell(k)^2.