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A347072
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E.g.f.: -log(1 - x) * (sec(x) + tan(x)).
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0
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0, 1, 3, 8, 28, 119, 605, 3597, 24624, 191481, 1672273, 16240509, 173870156, 2036293453, 25910852669, 356057435177, 5255621683776, 82932788545297, 1393129225943169, 24819194946609589, 467369450831456492, 9274872837974110805, 193447045984755732413
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OFFSET
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0,3
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COMMENTS
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Boustrophedon transform of shifted factorial numbers.
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LINKS
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FORMULA
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MATHEMATICA
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nmax = 22; CoefficientList[Series[-Log[1 - x] (Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := If[n == 0, 0, (n - 1)!]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Table[a[n], {n, 0, 22}]
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PROG
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(Python)
from itertools import accumulate, count, islice
def A347072_gen(): # generator of terms
blist, m = (0, ), 1
yield from blist
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= i
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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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