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A231894
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Boustrophedon transform of the Catalan numbers A000108.
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1
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1, 3, 10, 37, 149, 648, 3039, 15401, 84619, 505500, 3287256, 23250514, 178382427, 1478782490, 13187788246, 125958159631, 1283067859947, 13886218459612, 159124624924418, 1924735353849082, 24506483918914367, 327627501208785322
(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 44-54 1996 (Abstract, pdf, ps).
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FORMULA
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E.g.f.: exp(2*x)*I_1(2*x)*(sec(x)+tan(x))/x, where I_1(2*x) is the modified Bessel function of the first kind. - Sergei N. Gladkovskii, Nov 19 2014
a(n) ~ n! * exp(Pi) * BesselI(1, Pi) * 2^(n+3) / Pi^(n+2). - Vaclav Kotesovec, Jun 12 2015
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EXAMPLE
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G.f. = 1 + 3*x + 10*x^2 +37*x^3 + 149*x^4 + 648*x^5 + 3039*x^6 + 15401*x^7 + ...
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MAPLE
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option remember;
sec(x)+tan(x) ;
coeftayl(%, x=0, n)*n! ;
end proc:
end proc:
end proc:
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PROG
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(Python)
from itertools import accumulate, count, islice
def A231894_gen(): # generator of terms
blist, c = tuple(), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=c)))[-1]
c = c*(4*i+2)//(i+2)
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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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