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A000732
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Boustrophedon transform of 1 & primes: 1,2,3,5,7,...
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5
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1, 3, 8, 22, 66, 222, 862, 3838, 19542, 111894, 712282, 4987672, 38102844, 315339898, 2810523166, 26838510154, 273374835624, 2958608945772, 33903161435148, 410085034127000, 5221364826476796, 69804505809732988
(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.: (sec(x) + tan(x))*(1 + Sum_{k>=1} prime(k)*x^k/k!). -Ilya Gutkovskiy,Apr 23 2019
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MATHEMATICA
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t[n_, 0]:= If[n==0, 1, Prime[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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(Haskell)
a000732 n = sum $ zipWith (*) (a109449_row n) a008578_list
(Python)
from itertools import accumulate, count, islice
from sympy import prime
defA000732_gen(): # generator of terms
yield 1
blist = (1, )
for i in count(1):
yield (blist:= tuple(accumulate(reversed(blist), initial=prime(i))))[-1]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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