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A337447
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E.g.f.: exp(exp(x) - 1) / (sec(x) + tan(x)).
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1
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1, 0, 1, 0, 4, -4, 31, -144, 379, -5560, 8572, -263128, 473485, -15744416, 47003477, -1206879556, 5944492012, -119190424496, 876847239971, -15100821637664, 149690044061351, -2416631748015804, 29675481449346820, -477579212590451988, 6840036862556737337
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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Inverse boustrophedon transform of Bell numbers.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A000110(k) * A000111(n-k).
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MATHEMATICA
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nmax = 24; CoefficientList[Series[Exp[Exp[x] - 1]/(Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
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]; Table[a[n], {n, 0, 24}]
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PROG
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(Python)
from itertools import islice, accumulate
from operator import sub
def A337447_gen(): # generator of terms
yield from (1, 0)
blist, alist = (1, 0), (1, )
while True:
yield (blist := tuple(accumulate(reversed(blist), func=sub, initial=(alist := list(accumulate(alist, initial=alist[-1])))[-1])))[-1]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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