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A337446
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E.g.f.: exp(2*x) * (BesselI(0,2*x) - BesselI(1,2*x)) / (sec(x) + tan(x)).
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0
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1, 0, 1, 0, 3, -9, 5, -235, 35, -5939, 10773, -199746, 961521, -10506833, 82135911, -836458064, 8282576627, -90730736923, 1034615625645, -12538466040640, 159529541334325, -2133316798885373, 29875632576041747, -437461119834677379, 6683837093985315589
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OFFSET
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0,5
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COMMENTS
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Inverse boustrophedon transform of Catalan 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) * A000108(k) * A000111(n-k).
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MATHEMATICA
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nmax = 24; CoefficientList[Series[Exp[2 x] (BesselI[0, 2 x] - BesselI[1, 2 x])/(Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := CatalanNumber[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, count, accumulate
from operator import sub
def A337446_gen(): # generator of terms
blist, c = tuple(), 1
for i in count(0):
yield (blist := tuple(accumulate(reversed(blist), func=sub, initial=c)))[-1]
c = c*(4*i+2)//(i+2)
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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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