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A000764
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Boustrophedon transform of Bell numbers.
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3
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1, 2, 5, 16, 60, 258, 1247, 6686, 39371, 252688, 1756920, 13168178, 105949517, 911834394, 8367625793, 81642384468, 844718036940, 9245285569526, 106790005796627, 1298920385093126, 16602066548692623
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A (1996) 44-54 (Abstract, pdf, ps).
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FORMULA
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E.g.f.: (tan(x) + sec(x))*exp(exp(x) - 1).
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EXAMPLE
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The array begins:
1
1 -> 2
5 <- 4 <- 2
5 -> 10 -> 14 -> 16
60 <- 55 <- 45 <- 31 <- 15
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MATHEMATICA
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t[n_, 0] := BellB[n]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 30, 0] (* Jean-François Alcover, Feb 12 2016 *)
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PROG
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(Python)
from itertools import accumulate, islice
def A000764_gen(): # generator of terms
blist, alist = (1, 2), (1, )
yield from blist
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=(alist := list(accumulate(alist, initial=alist[-1])))[-1])))[-1]
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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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