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A000753
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Boustrophedon transform of Catalan numbers.
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8
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1, 2, 5, 16, 59, 243, 1101, 5461, 29619, 175641, 1137741, 8031838, 61569345, 510230087, 4549650423, 43452408496, 442620720531, 4790322653809, 54893121512453, 663974736739232, 8453986695437957, 113021461431438475
(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))*exp(2*x)*(BesselI(0,2*x) - BesselI(1,2*x)). - Sergei N. Gladkovskii, Oct 30 2014
a(n) ~ n! * exp(Pi) * (BesselI(0, Pi) - BesselI(1, Pi)) * 2^(n+2) / Pi^(n+1). - Vaclav Kotesovec, Oct 30 2014
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MATHEMATICA
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CoefficientList[Series[E^(2*x) * (BesselI[0, 2*x] - BesselI[1, 2*x]) * (Sec[x] + Tan[x]), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 30 2014 after Sergei N. Gladkovskii *)
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PROG
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(Haskell)
a000753 n = sum $ zipWith (*) (a109449_row n) a000108_list
(Python)
from itertools import accumulate, count, islice
def A000753_gen(): # generator of terms
blist, c = tuple(), 1
for i in count(0):
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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