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A217144 Alternating sums of squares of Bell numbers (A000110). 1
1, 0, 4, 21, 204, 2500, 38709, 730420, 16409180, 430786429, 13019414196, 447437830704, 17306961847705, 746907935199264, 35695643204860420, 1876878693983656605, 107956500727342113004, 6758630146906528885412, 458470139353155531447869 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k)*Bell(k)^2.
PROG
(Maxima) makelist(sum((-1)^(n-k)*belln(k)^2, k, 0, n), n, 0, 30);
(Python)
from itertools import accumulate, islice
def A217144_gen(): # generator of terms
yield 1
blist, b, c, f = (1, ), 1, 1, 1
while True:
blist = list(accumulate(blist, initial=(b:=blist[-1])))
yield (f:=-f)*(c := c+f*b**2)
A217144_list = list(islice(A217144_gen(), 20)) # Chai Wah Wu, Jun 22 2022
CROSSREFS
Sequence in context: A360630 A041667 A286883 * A132684 A357857 A032074
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Sep 27 2012
STATUS
approved

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Last modified July 13 12:36 EDT 2024. Contains 374284 sequences. (Running on oeis4.)