The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A217144 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A217144

Alternating sums of squares of Bell numbers (A000110).
(history; published version)

#12 by Michael De Vlieger at Wed Jun 22 14:49:41 EDT 2022

STATUS

proposed

approved

#11 by Michel Marcus at Wed Jun 22 13:01:58 EDT 2022

STATUS

editing

proposed

#10 by Michel Marcus at Wed Jun 22 13:01:49 EDT 2022

FORMULA

a(n) = sum(Sum_{k=0..n} (-1)^(n-k)*Bell(k)^2, k=0..n).

STATUS

proposed

editing

#9 by Chai Wah Wu at Wed Jun 22 13:00:57 EDT 2022

STATUS

editing

proposed

#8 by Chai Wah Wu at Wed Jun 22 13:00:33 EDT 2022

PROG

(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

STATUS

approved

editing

#7 by Bruno Berselli at Fri Sep 28 04:31:20 EDT 2012

STATUS

editing

approved

#6 by Bruno Berselli at Fri Sep 28 04:31:16 EDT 2012

DATA

1, 0, 4, 21, 204, 2500, 38709, 730420, 16409180, 430786429, 13019414196, 447437830704, 17306961847705, 746907935199264, 35695643204860420, 1876878693983656605, 107956500727342113004, 6758630146906528885412, 458470139353155531447869, 33562411491300039104925380

#5 by Bruno Berselli at Fri Sep 28 04:31:01 EDT 2012

DATA

#4 by Bruno Berselli at Fri Sep 28 04:30:30 EDT 2012

NAME

Alternating sums of squares of Bell numbers (A000110).

FORMULA

a(n) = sum((-1)^(n-k)*Bell(k)^2, k,=0,..n).

PROG

(Maxima) makelist(sum((-1)^(n-k)*belln(k)^2, k, 0, n), n, 0, 30);

CROSSREFS

Cf. A000110, A005001, A087650, A217143.

STATUS

proposed

editing

#3 by Emanuele Munarini at Thu Sep 27 06:08:26 EDT 2012

STATUS

editing

proposed