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A307879
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Expansion of e.g.f. exp(4*x)*(sec(x) + tan(x)).
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1
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1, 5, 25, 126, 645, 3380, 18285, 103036, 610345, 3833540, 25714345, 185107596, 1433220045, 11932724900, 106613406405, 1019012112556, 10382757537745, 112378069315460, 1287787864054465, 15576862520435916, 198330820236011445, 2651486893149253220, 37135749401704458525
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OFFSET
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0,2
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COMMENTS
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Boustrophedon transform of A000302 (powers of 4).
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LINKS
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MATHEMATICA
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nmax = 22; CoefficientList[Series[Exp[4 x] (Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := 4^n; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 23, 0]
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PROG
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(Python)
from itertools import accumulate, islice
def A307879_gen(): # generator of terms
blist, m = tuple(), 1
yield from blist
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= 4
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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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