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A217143
Sum of squares of Bell numbers (A000110).
1
1, 2, 6, 31, 256, 2960, 44169, 813298, 17952898, 465148507, 13915349132, 474372594032, 18228772272441, 782443669319410, 37224994809379094, 1949799331997896119, 111783178753323665728, 6978369826387194664144, 472207139326449254997425
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} Bell(k)^2.
MATHEMATICA
Accumulate[BellB[Range[0, 20]]^2] (* Bruno Berselli, Sep 27 2012 *)
PROG
(Maxima) makelist(sum(belln(k)^2, k, 0, n), n, 0, 30);
(Magma) [&+[Bell(i)^2: i in [0..n]]: n in [0..20]]; // Bruno Berselli, Sep 27 2012
(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
CROSSREFS
Partial sums of A001247.
Sequence in context: A113719 A369767 A018225 * A075845 A003087 A203901
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Sep 27 2012
STATUS
approved