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A337443
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E.g.f.: (1 + x) * exp(x) / (sec(x) + tan(x)).
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0
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1, 1, 0, -1, -4, -5, -20, 9, -208, 855, -6180, 41549, -321792, 2651155, -23664420, 225865769, -2301032256, 24901626095, -285356879940, 3451591584869, -43947119045600, 587529302036875, -8228722825167940, 120487046847246049, -1840906518665985824
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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 positive natural 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) * (k+1) * A000111(n-k).
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MATHEMATICA
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nmax = 24; CoefficientList[Series[(1 + x) Exp[x]/(Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 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, 24}]
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PROG
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(Python)
from itertools import count, islice, accumulate
from operator import sub
def A337443_gen(): # generator of terms
blist = tuple()
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), func=sub, initial=i)))[-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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