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A217144
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Alternating sums of squares of Bell numbers (A000110).
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1
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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)
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (-1)^(n-k)*Bell(k)^2.
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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