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

0,2

Links

Table of n, a(n) for n=0..18.

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

Cf. A000110, A005001, A087650, A217144.

Partial sums of A001247.

Sequence in context: A113719 A369767 A018225 * A075845 A003087 A203901

Adjacent sequences: A217140 A217141 A217142 * A217144 A217145 A217146

Keyword

nonn

Author

Emanuele Munarini, Sep 27 2012

Status

approved