A217144 Alternating sums of squares of Bell numbers (A000110).

1, 0, 4, 21, 204, 2500, 38709, 730420, 16409180, 430786429, 13019414196, 447437830704, 17306961847705, 746907935199264, 35695643204860420, 1876878693983656605, 107956500727342113004, 6758630146906528885412, 458470139353155531447869

Offset

0,3

Links

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

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

Cf. A000110, A005001, A087650, A217143.

Sequence in context: A041667 A377828 A286883 * A132684 A357857 A032074

Adjacent sequences: A217141 A217142 A217143 * A217145 A217146 A217147

Keyword

nonn

Author

Emanuele Munarini, Sep 27 2012

Status

approved